Pubblicazioni

[R1]

M. Paolini, G. Sacchi, and C. Verdi, Finite element approximation of singular parabolic problems, Internat. J. Numer. Methods Engrg., 26 (1988), 1989--2007.

[RT1]

M. Paolini, G. Sacchi, and C. Verdi, Approssimazione di problemi a frontiera libera parabolici con metodi ad elementi finiti, Public. IAN - CNR, Pavia, 556 (1987), 1--19.

[RT2]

M. Paolini, G. Sacchi, and C. Verdi, Approssimazione numerica di problemi parabolici a frontiera libera con metodi ad elementi finiti e visualizzazione grafica dei risultati: guida all'uso dei moduli GINT, GEO e STEF, Public. IAN - CNR, Pavia, 576 (1987), 1--119.

[RT3]

M. Paolini and C. Verdi, Un generatore automatico di reticolazioni triangolari per domini piani, Public. IAN - CNR, Pavia, 614 (1988), 1--21.

[R2]

M. Paolini and C. Verdi, An automatic triangular mesh generator for planar domains, Riv. Inform., 20 (1990), 251--267.

[R3]

S. Mazzullo, M. Paolini, and C. Verdi, Polymer crystallization and processing: free boundary problems and their numerical approximation, Math. Engng. Ind., 2 (1989), 219--232.

[C1]

S. Mazzullo, M. Paolini, and C. Verdi, Numerical approximation of free boundary problems in polymer crystallization, Proc. Third European Conference on Mathematics in Industry (Glasgow, 1988, J. Manley et al., eds.), Kluwer Academic Publisher and G.B. Teubner, Stuttgart (1990), 437--443.

[R4]

L. Carrioli, M. Diani, and M. Paolini, Shortest path search: a formalization and a parallel implementation, Public. IAN - CNR, Pavia, 716 (1989), 1--29.

[C2]

M. Paolini, G. Sacchi, and C. Verdi, Approssimazione del problema di Stefan con metodi agli elementi finiti e tecniche adattive, Atti Convegno Nazionale di Analisi Numerica (Roma, 1988), pubblic. Dip. Metodi e Modelli Matematici per le Scienze Applicate, Roma (1988), 365--372.

[C3]

R.H. Nochetto, M. Paolini, and C. Verdi, Local mesh refinements for two-phase Stefan problems in two space variables, Mathematical Models for Phase Change Problems (J.F. Rodrigues ed.), Birkh\"auser, Basel (1989), 261--286.

[C4]

R.H. Nochetto, M. Paolini, and C. Verdi, An adaptive finite element method for Stefan problems, Proc. Fourth European Conference on Mathematics in Industry (St. Wolfgang, 1989, Hj. Wacker et al., eds.), Kluwer Academic Publisher and G.B. Teubner, Stuttgart (1991), 347--352.

[C5]

R.H. Nochetto, M. Paolini, and C. Verdi, Selfadaptive mesh modification for parabolic FBPs: theory and computation, Proc. Free Boundary Problems (Oberwolfach, 1989, K.H. Hoffmann and J. Sprekels, eds.), Birkh\"auser, Basel (1990), 181--206.

[C6]

R.H. Nochetto, M. Paolini, and C. Verdi, Quasi-optimal mesh adaptation for two-phase Stefan problems in 2D, Proc. Computational Mathematics and Applications, 8th France-USSR-Italy Joint Symposium (E. Magenes ed.), Public. IAN - CNR, Pavia, 730 (1989), 313--326.

[C7]

G. Bellettini, M. Paolini, and C. Verdi, Convergence of discrete approximations to sets of prescribed mean curvature, Free boundary problems involving solids (J.M. Chadam and H. Rasmussen, eds.), Longman Scientific \& Technical, Harlow (1993), 164--169.

[C8]

R.H. Nochetto, M. Paolini, and C. Verdi, Basic principles of mesh adaptation for parabolic FBPs, Free boundary problems involving solids (J.M. Chadam and H. Rasmussen, eds.), Longman Scientific \& Technical, Harlow (1993), 177--182.

[C9]

R.H. Nochetto, M. Paolini, and C. Verdi, Efficient mesh adaptation for parabolic FBPs, Free boundary problems involving solids (J.M. Chadam and H. Rasmussen, eds.), Longman Scientific \& Technical, Harlow (1993), 183--189.

[R5]

R.H. Nochetto, M. Paolini, and C. Verdi, An adaptive finite elements method for two-phase Stefan problems in two space dimensions. Part I: stability and error estimates, Math. Comp., 57 (1991), 73--108.

[R6]

R.H. Nochetto, M. Paolini, and C. Verdi, An adaptive finite elements method for two-phase Stefan problems in two space dimensions. Part II: implementation and numerical experiments, SIAM J. Sci. Statist. Comput., 12 (1991), 1207--1244.

[R7]

S. Mazzullo, M. Paolini, and C. Verdi, Numerical simulation of thermal bone necrosis during cementation of femoral prostheses, J. Math. Biol., 29 (1991), 475--494.

[C10]

R.H. Nochetto, M. Paolini, and C. Verdi, Design and efficient implementation of an adaptive FEM for parabolic FBPs, Numerical Methods for Free Boundary Problems (P. Neittaanm\"aki ed.), Birkh\"auser, Basel (1991), 325--335.

[C11]

S. Mazzullo, M. Paolini, and C. Verdi, An axisymmetric analysis of thermal effects during cementation of femoral prostheses, Proc. Conference on Numerical Methods for Free Boundary Problems (Jyv\"askyl\"a, 1990, P. Neittaanm\"aki ed.), Birkh\"auser, Basel (1991), 259--269.

[C12]

G. Bellettini, M. Paolini, and C. Verdi, Front-tracking and variational methods to approximate interfaces with prescribed mean curvature, Numerical Methods for Free Boundary Problems (Jyv\"askyl\"a, 1990), Birkh\"auser, Basel (1991), 83--92.

[C13]

S. Mazzullo, M. Paolini, and C. Verdi, Simulazione numerica di modelli di cambiamento di fase nella solidificazione dei po\-li\-me\-ri, Proc. Convegno Modelli Matematici ed Esperimenti di Cristallizzazione dei Polimeri (Ferrara, 1990), Himont Italia, Ferrara (1990), 59--65.

[R8]

G. Bellettini, M. Paolini, and C. Verdi, $\Gamma$-convergence of discrete approximations to interfaces with prescribed mean curvature, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 1 (1990), 317--328.

[RT4]

M. Paolini and S. Tentoni, TEK2PS: Un programma per la conversione di files grafici Tektronix in procedure PostScript., Public. IAN - CNR, Pavia, 778 (1991), 1--23.

[R9]

G. Bellettini, M. Paolini, and C. Verdi, Numerical minimization of geometrical type problems related to calculus of variations, Calcolo, 27 (1991), 251--278.

[R10]

G. Bellettini, M. Paolini, and C. Verdi, Convex approximations of functionals with curvature, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 2 (1991), 297--306.

[C14]

G. Bellettini, M. Paolini, and C. Verdi, Numerical minimization of functionals with curvature by convex approximations, Progress in partial differential equations: calculus of variations, applications (C. Bandle {\it et al.}, eds.), Longman, Harlow (1992), 124--138.

[R11]

M. Paolini and C. Verdi, Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter, Asymptotic Anal., 5 (1992), 553--574.

[C15]

R.H. Nochetto, M. Paolini, and C. Verdi, Towards a unified approach for the adaptive solution of evolution phase changes, Variational and Free Boundary Problems (A. Friedman and J. Spruck, eds.), Springer, New York (1993), 171--193.

[C16]

G. Bellettini, M. Paolini, and C. Verdi, $\Gamma$-convergence and numerical approximation of interface problems, Proc. 9th France-USSR-Italy Joint Symposium in Computational Mathematics and Applications (Sophia-Antipolis, France, 1991) (1991), 23--46.

[R12]

R.H. Nochetto, M. Paolini, and C. Verdi, A fully discrete adaptive nonlinear Chernoff formula, SIAM J. Numer. Anal., 30, 4, (1993), 991--1014.

[R13]

G. Bellettini, G. Dal Maso, and M. Paolini, Semicontinuity and relaxation properties of a curvature depending functional in 2D, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 20 (1993), 247--297.

[R14]

R.H. Nochetto, M. Paolini, and C. Verdi, Continuous and semidiscrete travelling waves for a phase relaxation model, European J. Appl. Math., 5 (1994), 177--199.

[RT5]

S. Mazzullo, M. Paolini, and C. Verdi, Modelli, esperimenti e simulazione di cristallizzazione di polimeri, Preprint (1992).

[R15]

R.H. Nochetto, M. Paolini, and C. Verdi, Optimal interface error estimates for the mean curvature flow, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 21 (1994), 193--212.

[R16]

R.H. Nochetto, M. Paolini, and C. Verdi, Sharp error analysis for curvature dependent evolving fronts, Math. Models Methods Appl. Sci., 3 (1993), 711--723.

[RT6]

D. Andreucci, A. Fasano, M. Paolini, M. Primicerio, and C. Verdi, Numerical simulation of polymer crystallization, Math. Models Methods Appl. Sci., 4 (1994), 135--145.

[C17]

R.H. Nochetto, M. Paolini, S. Rovida, and C. Verdi, Variational approximation of the geometric motion of fronts, Motion by Mean Curvature and Related Topics (G. Buttazzo and A. Visintin, eds.), Gruyter, Berlin (1994), 124--149.

[C18]

R.H. Nochetto, M. Paolini, and C. Verdi, Geometric motion of interfaces, Boundary value Problems for Partial Differential Equations and Applications (J.-L. Lions, C. Baiocchi, eds.), Masson, Paris (1993), 403--408.

[C19]

R.H. Nochetto, M. Paolini, and C. Verdi, Linearization and adaptivity for FBPs, Boundary value Problems for Partial Differential Equations and Applications (J.-L. Lions, C. Baiocchi, eds.), Masson, Paris (1993), 443--447.

[R17]

R.H. Nochetto, M. Paolini, and C. Verdi, Double obstacle formulation with variable relaxation parameter for smooth geometric front evolutions: asymptotic interface error estimates, Asymptotic Anal., 10 (1995), 173--198.

[C20]

G. Bellettini and M. Paolini, Approssimazione variazionale di funzionali con curvatura, Seminario di Analisi Matematica, Dipartimento di Matematica dell'Universit\`a di Bologna, 11 marzo (1993), 87--97.

[R18]

G. Bellettini and M. Paolini, Quasi-optimal error estimates for the mean curvature flow with a forcing term, Differential Integral Equations, 8 (1995), 735--752.

[R19]

G. Bellettini and M. Paolini, Variational properties of an image segmentation functional depending on contours curvature, Adv. Math. Sci. Appl., 5 (1995), 681--715.

[R20]

G. Bellettini and M. Paolini, Convex approximations of an inhomogeneous anisotropic functional, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 5 (1994), 177--187.

[R21]

G. Bellettini and M. Paolini, Numerical simulations of measurements of capillary contact angles, IMA J. Numer. Anal., 16 (1996), 165--178.

[R22]

R.H. Nochetto, M. Paolini, and C. Verdi, Quadratic rate of convergence for curvature dependent smooth interfaces: a simple proof, Appl. Math. Lett., 7 (1994), 59--63.

[R23]

G. Bellettini and M. Paolini, Two examples of fattening for the curvature flow with a driving force, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 5 (1994), 229--236.

[RT7]

R. Caselli, S. Mazzullo, M. Paolini, and C. Verdi, Models, experiments, and numerical simulation of isothermal crystallization of polymers, Proceedings of the Seventh European Conference on Mathematics in Industry, March 2-6, 1993 Montecatini Terme (A. Fasano and M. Primicerio, eds.), B. G. Teubner, Stuttgart (1994), 167--174.

[RT8]

G. Bellettini and M. Paolini, Su un modello di Mumford e Nitzberg per la segmentazione di immagini, Seminario di Analisi Matematica, Dipartimento di Matematica dell'Universit\`a di Bologna, 28 aprile (1994), 72--85.

[R24]

R.H. Nochetto, M. Paolini, and C. Verdi, A dynamic mesh algorithm for curvature dependent evolving interfaces, J. Comput. Phys., 123 (1996), 296--310.

[R25]

G. Bellettini, M. Paolini, and S. Venturini, Some results on surface measures in Calculus of Variations, Ann. Mat. Pura Appl., 170 (1996), 329--359.

[R26]

M. Paolini, A quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem, Math. Comp., 66 (1997), 45--67.

[R27]

G. Bellettini and M. Paolini, Teoremi di confronto tra diverse nozioni di movimento secondo la curvatura media, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 6 (1995), 45--54.

[R28]

G. Bellettini and M. Paolini, Anisotropic motion by mean curvature in the context of Finsler geometry, Hokkaido Math. J., 25 (1996), 537--566.

[R29]

F. Fierro, R. Goglione, and M. Paolini, Finite element minimization of curvature functionals with anisotropy, Calcolo, 3-4 (1994), 191--210.

[C21]

M. Paolini, An efficient algorithm for computing anisotropic evolution by mean curvature, Curvature Flows and Related Topics (A. Damlamian {\it et al.}, eds.), Gakk\"otosho, Tokyo (1995), 199--213.

[R30]

G. Bellettini and M. Paolini, Some results on minimal barriers in the sense of De Giorgi applied to driven motion by mean curvature, Rend. Accad. Naz. Sci. XL Mem. Mat. (5), 19 (1995), 43--67.

[R31]

F. Fierro and M. Paolini, Numerical evidence of fattening for the mean curvature flow, Math. Models Methods Appl. Sci., 6 (1996), 793--813.

[R32]

C.M. Elliott, M. Paolini, and R. Sch\"atzle, Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean curvature flow, Math. Models Methods Appl. Sci., 6 (1996), 1103--1118.

[C22]

R. Goglione and M. Paolini, Numerical simulations of crystalline motion by mean curvature with Allen-Cahn relaxation, Free boundary problems, theory and applications (M. Niezg\'odka and P. Strzelecki, eds.), Longman Scientific \& Technical, Harlow (1996), 203--216.

[R33]

G. Bellettini, P. Colli Franzone, and M. Paolini, Convergence of front propagation for anisotropic bistable reaction-diffusion equations, Asymptot. Anal., 15 (1997), 325--358.

[R34]

F. Fierro, R. Goglione, and M. Paolini, Numerical simulations of mean curvature flow in presence of a nonconvex anisotropy, Math. Models Methods Appl. Sci., 4 (1998), 573--601.

[R35]

G. Bellettini, M. Novaga, and M. Paolini, An example of three dimensional fattening for linked space curves evolving by curvature, Comm. Partial Differential Equations, 23 (1998), 1475--1492.

[R36]

B. Cecon, M. Paolini, and M. Romeo, Optimal interface error estimates for a discrete double obstacle approximation to the prescribed curvature problem, Math. Models Methods Appl. Sci., 9 (1999), 799--823.

[C23]

M. Paolini, Fattening in two dimensions obtained with a nonsymmetric anisotropy: numerical simulations, Acta Math. Univ. Comenianae, 67 (1998), 43--55.

[R37]

G. Bellettini, M. Novaga, and M. Paolini, Facet-breaking for three dimensional crystals evolving by mean curvature, Interfaces and Free Boundaries, 1 (1999), 39--55.

[R38]

G. Bellettini, M. Novaga, and M. Paolini, On a crystalline variational problem, part I: first variation and global $L^\infty$-regularity, Arch. Ration. Mech. Anal., 3 (2001), 165--191.

[C24]

M. Paolini and F. Pasquarelli, Numerical simulation of crystalline curvature flow in 3D by interface diffusion, Free Boundary Problems: theory and applications II (N. Kenmochi ed.), Gakk\"otosho, Tokyo (2000), 376--389.

[R39]

M. Negri and M. Paolini, Numerical minimization of the Mumford-Shah functional, Calcolo, 38 (2001), 67--84.

[R40]

G. Bellettini, M. Novaga, and M. Paolini, Characterization of facet--breaking for nonsmooth mean curvature flow in the convex case, Interfaces and Free Boundaries, 3 (2001), 415--446.

[R41]

G. Bellettini, M. Novaga, and M. Paolini, On a crystalline variational problem, part II: $BV$-regularity and structure of minimizers on facets, Arch. Ration. Mech. Anal., 3 (2001), 193--217.

[R42]

Y. Giga, M. Paolini, and P. Rybka, On the motion by singular interfacial energy, Japan J. Indust. Appl. Math., 18 (2001), 47--64.

[C25]

M. Paolini and F. Pasquarelli, Unstable Crystalline Wulff Shapes in 3D, Proceedings Variational methods for discontinuous structures, Birkhauser, Basel (2002), 141--153.

[R43]

G. Bellettini and M. Paolini, Errata corrige to the paper: Some results on minimal barriers in the sense of De Giorgi applied to driven motion by mean curvature, Rend. Accad. Naz. Sci. XL Mem. Mat. (5), 26 (2002), 161--165.

[LN1]

M. Paolini, From the Stefan problem to crystalline evolution, FM-DM Lecture notes, Warsaw, july 2002 (2002), 1--31.

[D1]

A. Forlini and M. Paolini, Fidarsi dei software di geometria interattiva?, Ricordando Franco Conti (Fulvio Ricci, Mariano Giacquinta, Alberto Abbondandolo, eds.), Scuola Normale Superiore, Pisa (2004), 181--193.

[C26]

M. Paolini, Capillarity and calibrability of sets in crystalline mean curvature flow, Oberwolfach Reports, 2 (2005), 560--562.

[R44]

M. Novaga and M. Paolini, Nonuniqueness for crystalline curvature flow, Math. Models Methods Appl. Sci., 17 (2007), 1307--1315.

[R45]

G. Bellettini, V. Beorchia, and M. Paolini, Topological and variational properties of a model for the reconstruction of three-dimensional transparent images with self-occlusions, J. Math. Imaging Vision, 32 (2008), 265--291.

[R48]

G. Bellettini, M. Novaga, M. Paolini, and C. Tornese, Convergence of discrete schemes for the Perona-Malik equation, J. Differential Equations, 245 (2008), 892--924.

[C27]

M. Paolini, A software code to manipulate apparent contours, Oberwolfach Reports, 4 (2007), 179--181.

[R47]

G. Bellettini, V. Beorchia, and M. Paolini, An explicit formula for a Bennequin-type invariant for apparent contours, Topology Appl., 156 (2009), 747--760.

[R49]

G. Bellettini, M. Novaga, M. Paolini, and C. Tornese, Classification of the equilibria for the semi-discrete Perona-Malik equation, Calcolo, 46 (2009), 221--243.

[R52]

G. Bellettini, M. Novaga, and M. Paolini, Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension, Math. Models Methods Appl. Sci., 21 (2011), 241--265.

[R50]

G. Bellettini, V. Beorchia, and M. Paolini, Completion of visible contours, SIAM J. Imaging Sci., 2 (2009), 777--799.

[R51]

G. Bellettini, V. Beorchia, and M. Paolini, Completeness of Reidemeister-type moves for surfaces embedded in three-dimensional space, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 23 (2012), 69--87.

[R53]

G. Bellettini and M. Paolini, On the area of the graph of a singular map from the plane to the plane taking three values, Adv. Calc. Var., 3 (2010), 371–-386.

[C28]

M. Paolini, Nonconvex anisotropy and the bidomain model, Proc. Geometric Partial Differential Equations: Theory, Numerics and Applications (Oberwolfach, 2011), Oberwolfach Reports, 54 (2011), 52--54.

[R54]

G. Bellettini, M. Paolini, and F. Pasquarelli, Nonconvex mean curvature flow as a formal singular limit of the nonlinear bidomain model, Adv. Differential Equations, 18 (2013), 895--934.

[C29]

S. Amato, G. Bellettini, and M. Paolini, The nonlinear multidomain model: a new formal asymptotic analysis, Proc. Geometric Partial Differential Equations (Pisa, Italy, 2012, A. Chambolle, M. Novaga, E. Valdinoci, eds.), Edizioni della Normale, Pisa (2013), 33--74.

[R55]

G. Bellettini, M. Paolini, and L. Tealdi, On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity, ESAIM: Control, Optimisation and Calculus of Variations, 22 (2016), 29--63.

[R56]

A. Musesti, M. Paolini, and C. Reale, An optimal bound on the number of moves for open Mancala, Discrete Math, 338 (2015), 1827--1844.

[B1]

G. Bellettini, V. Beorchia, M. Paolini, and F. Pasquarelli, Shape Reconstruction from Apparent Contours. Theory and Algorithms, Springer Verlag, Berlin (2015).

[D2]

M. Paolini, Exploring the "Rubik's Magic" universe, Recreat. Math. Mag., 4 (2017), 29--64.

[R57]

S. Amato, G. Bellettini, and M. Paolini, Constrained BV functions on covering spaces for minimal networks and Plateau's type problems, Adv. Calc. Var., 10 (2017), 25--47.

[R58]

G. Bellettini, M. Paolini, and L. Tealdi, Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity, Ann. Mat. Pura Appl., 195 (2016), 2131–2170.

[D3]

M. Paolini, L'eredità di Martin Gardner, Alice & Bob, 49 (2017), 57--64.

[D4]

M. Paolini, Gli anelli che ruzzolano, Alice & Bob, 49 (2017), 73--79.

[R59]

G. Bellettini, M. Paolini, and F. Pasquarelli, Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone, Interfaces and Free Boundaries, 20 (2018), 407--436.

[C30]

G. Bellettini, M. Paolini, F. Pasquarelli, and G. Scianna, Covers, soap films and BV functions, Geometric Flows, 3 (2018), 57--75.

[R60]

G. Bellettini, A. Elshorbagy, M. Paolini, and R. Scala, On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions, Ann. Mat. Pura Appl. (2019), 1--33, online-first.

[R61]

G. Bellettini, M. Paolini, and Y.-S. Wang, A complete invariant for connected surfaces in the 3-sphere, J. Knot Theory Ramifications, 29 (2020), 1--24.

[R62]

G. Bellettini, M. Paolini, and Y.-S. Wang, A complete invariant for closed surfaces in the three-sphere, J. Knot Theory Ramifications, 30 (2021), 1--25.

[R63]

G. Bellettini, M. Paolini, and Y.-S. Wang, Numerical irreducibility criteria for handlebody links, Topology and its Applications, 284 (2020), 1--14.

[R64]

G. Bellettini, G. Paolini, M. Paolini, and Y.-S. Wang, A table of n-component handlebody links of genus n plus 1 up to six crossings, Math. Proc. Cambridge Philos. Soc., 174 (2023).

[R65]

A. Marzocchi, M. Paolini, F. Pasquarelli, and P. Tesini, Multimodelling simulation of external water inflows into a morainic lake: the Lake Garda case, Far East Journal of Applied Mathematics, 107 (2020), 107--130.

[R66]

G. Bellettini, A. Betti, and M. Paolini, A free boundary singular transport equation as a formal limit of a discrete dynamical system, J. Differential Equations, to appear.