Abstract
Using recent results proved in [8], we continue the analysis initiated in [5] of two explicit examples of facet breaking/bending of a polyhedral set evolving by crystalline mean curvature in three dimensions.
Similar content being viewed by others
References
G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. 135 (1983), 293–318.
G. Bellettini, Anisotropic and crystalline mean curvature flow, Riemann-Finsler Geometry, MSRI Publications, Vol. 50, 2004, 51–84.
G. Bellettini, V. Caselles and M. Novaga, The total variation flow in R n, J. Differential Equations 184 (2002), 475–525.
G. Bellettini, V. Caselles and M. Novaga, Du ) — u, SIAM J. Math. Anal., (to appear).
G. Bellettini, M. Novaga and M. Paolini, Facet-breaking for three-dimensional crystals evolving by mean curvature, Interfaces Free Bound. 1 (1999), 39–55.
G. Bellettini, M. Novaga and M. Paolini, On a crystalline variational problem, part I: first variation and global L ∞-regularity, Arch. Rational Mech. Anal. 157 (2001) 3, 165–191.
G. Bellettini, M. Novaga and M. Paolini, On a crystalline variational problem, part II: BV-regularity and structure of minimizers on facets, Arch. Rational Mech. Anal. 157 (2001) 3, 193–217.
G. Bellettini, M. Novaga and M. Paolini, Characterization of facet-breaking for nonsmooth mean curvature flow in the convex case, Interfaces Free Bound. 3, (2001) 415–446.
M. Novaga and E. Paolini, A computational approach to fractures in crystal growth, Atti Acc. Lincei Cl. Sci. Fis. Mat. Natur. Ser. IX, X, 1999, 47–56.
M. Paolini and F. Pasquarelli, Numerical simulations of crystalline curvature flow in 3D by interface diffusion, in: Free Boundary Problems: theory and applications II, GAKUTO Intern. Ser. Math. Sci. Appl. 14 (ed. by N. Kenmochi), Gakkötosho, 2000, 376–389 (to appear).
J. Yunger, Facet stepping and motion by crystalline curvature, Ph.D. Thesis, Rutgers University, 1998.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bellettini, G. On facet breaking for crystalline mean curvature flow in 3D. Periodica Mathematica Hungarica 48, 185–206 (2004). https://doi.org/10.1023/B:MAHU.0000038975.39354.ef
Published:
Issue Date:
DOI: https://doi.org/10.1023/B:MAHU.0000038975.39354.ef