Existence and uniqueness for dislocation dynamics with nonnegative velocity, Interfaces and Free Boundaries, vol.7, pp.415-434, 2005. ,
DOI : 10.4171/IFB/131
Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution, Archive for Rational Mechanics and Analysis, vol.51, issue.3, pp.449-504, 2006. ,
DOI : 10.1007/s00205-006-0418-5
Solutions de viscosité deséquationsdeséquations de Hamilton-Jacobi, 1994. ,
Global Existence Results and Uniqueness for Dislocation Equations, SIAM Journal on Mathematical Analysis, vol.40, issue.1 ,
DOI : 10.1137/070682083
URL : https://hal.archives-ouvertes.fr/hal-00129352
Existence of weak solutions for general nonlocal equations ,
URL : https://hal.archives-ouvertes.fr/hal-00287372
Nonlocal First-Order Hamilton???Jacobi Equations Modelling Dislocations Dynamics, Communications in Partial Differential Equations, vol.6, issue.8, pp.311191-1208, 2006. ,
DOI : 10.1007/BFb0094298
URL : https://hal.archives-ouvertes.fr/hal-00021694
Front Propagation and Phase Field Theory, SIAM Journal on Control and Optimization, vol.31, issue.2, pp.439-469, 1993. ,
DOI : 10.1137/0331021
Vicosity solutions of fully nonlinear second order parabolic equations with L1-time dependence and neumann boundary conditions ,
Vicosity solutions of fully nonlinear second order parabolic equations with L1-time dependence and neumann boundary conditions. existence and applications to the level-set approach ,
The Maximum Principle under Minimal Hypotheses, SIAM Journal on Control and Optimization, vol.14, issue.6, pp.1078-1091, 1976. ,
DOI : 10.1137/0314067
Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.277, issue.1, pp.1-42, 1983. ,
DOI : 10.1090/S0002-9947-1983-0690039-8
Measure theory and fine properties of functions, Studies in Advanced Mathematics, 1992. ,
Global Existence of Weak Solutions for Interface Equations Coupled with Diffusion Equations, SIAM Journal on Mathematical Analysis, vol.23, issue.4, pp.821-835, 1992. ,
DOI : 10.1137/0523043
Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Fac. Sci. Eng. Chuo Univ, vol.28, pp.33-77, 1985. ,
Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts, Adv. Differential Equations, vol.6, issue.5, pp.547-576, 2001. ,
Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians, Nonlinear Analysis: Theory, Methods & Applications, vol.11, issue.5, pp.613-621, 1987. ,
DOI : 10.1016/0362-546X(87)90076-9
Integral formulations of the geometric eikonal equation. Interfaces Free Bound, pp.253-283, 2007. ,
Uniqueness of viscosity solutions of fully nonlinear second order parabolic equations with discontinuous time-dependence, Differential Integral Equations, vol.3, issue.1, pp.77-91, 1990. ,
Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence, Nonlinear Analysis: Theory, Methods & Applications, vol.18, issue.11, pp.1033-1062, 1992. ,
DOI : 10.1016/0362-546X(92)90194-J
Phase field methods and dislocations, Acta Materialia, vol.51, issue.1, pp.17-30, 2003. ,
DOI : 10.1016/S1359-6454(01)00379-2
URL : https://hal.archives-ouvertes.fr/hal-00125516
Phase-Field Theory for FitzHugh???Nagumo-Type Systems, SIAM Journal on Mathematical Analysis, vol.27, issue.5, pp.1341-1359, 1996. ,
DOI : 10.1137/S0036141094261318
Parc de Grandmont, 37200 Tours, France, {barles,ley}@lmpt.univ-tours, fr (P. Cardaliaguet, A. Monteillet) Laboratoire de Mathématiques, CNRS UMR 6205, 29285. ,