JournalsjemsVol. 10, No. 4pp. 1061–1104

Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics

  • Francesca Da Lio

    Università di Torino, Italy
  • Régis Monneau

    CERMICS - ENPC, Marne-La-Vallée, France
  • Nicolas Forcadel

    Université Paris-Dauphine, France
Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics cover

Abstract

In this paper we prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. This first order equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, that arises in the theory of dislocations dynamics. We show that if an anisotropic mean curvature motion is approximated by this type of equations then it is always of variational type, whereas the converse is true only in dimension two.

Cite this article

Francesca Da Lio, Régis Monneau, Nicolas Forcadel, Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics. J. Eur. Math. Soc. 10 (2008), no. 4, pp. 1061–1104

DOI 10.4171/JEMS/140