Skip to main content
Log in

On facet breaking for crystalline mean curvature flow in 3D

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. 135 (1983), 293–318.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Bellettini, Anisotropic and crystalline mean curvature flow, Riemann-Finsler Geometry, MSRI Publications, Vol. 50, 2004, 51–84.

  3. G. Bellettini, V. Caselles and M. Novaga, The total variation flow in R n, J. Differential Equations 184 (2002), 475–525.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Bellettini, V. Caselles and M. Novaga, Du ) — u, SIAM J. Math. Anal., (to appear).

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

    Article  MathSciNet  MATH  Google Scholar 

  6. 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.

    Article  MathSciNet  MATH  Google Scholar 

  7. 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.

    Article  MathSciNet  MATH  Google Scholar 

  8. 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.

    Article  MathSciNet  MATH  Google Scholar 

  9. 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.

    MathSciNet  MATH  Google Scholar 

  10. 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).

  11. J. Yunger, Facet stepping and motion by crystalline curvature, Ph.D. Thesis, Rutgers University, 1998.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:MAHU.0000038975.39354.ef

Navigation