Existence and uniqueness for dislocation dynamics with nonnegative velocity, Interfaces Free Bound, pp.415-434, 2005. ,
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
Set-valued analysis. Modern Birkhäuser Classics, 2009. ,
DOI : 10.1007/978-1-4612-1576-9_5
A new stability result for viscosity solutions of nonlinear parabolic equations with weak convergence in time, Comptes Rendus Mathematique, vol.343, issue.3, pp.173-178, 2006. ,
DOI : 10.1016/j.crma.2006.06.022
URL : https://hal.archives-ouvertes.fr/hal-00016437
A Geometrical Approach to the Study??of Unbounded Solutions??of Quasilinear Parabolic Equations, Archive for Rational Mechanics and Analysis, vol.162, issue.4, pp.287-325, 2002. ,
DOI : 10.1007/s002050200188
Global Existence Results and Uniqueness for Dislocation Equations, SIAM Journal on Mathematical Analysis, vol.40, issue.1, pp.44-69, 2008. ,
DOI : 10.1137/070682083
URL : https://hal.archives-ouvertes.fr/hal-00129352
Uniqueness results for nonlocal Hamilton???Jacobi equations, Journal of Functional Analysis, vol.257, issue.5, pp.1261-1287, 2009. ,
DOI : 10.1016/j.jfa.2009.04.014
URL : https://hal.archives-ouvertes.fr/hal-00264757
Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations, Nonlinear Anal, TMA, pp.71-2801, 2009. ,
Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations, Mathematics of Computation, vol.76, issue.260, pp.1861-1893, 2007. ,
DOI : 10.1090/S0025-5718-07-02000-5
URL : https://hal.archives-ouvertes.fr/hal-00017877
Nonlocal First-Order Hamilton???Jacobi Equations Modelling Dislocations Dynamics, Communications in Partial Differential Equations, vol.6, issue.8, pp.1191-1208, 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
A New Approach to Front Propagation Problems: Theory and Applications, Archive for Rational Mechanics and Analysis, vol.141, issue.3, pp.237-296, 1998. ,
DOI : 10.1007/s002050050077
Two examples of fattening for the curvature flow with a driving force, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Mat. Appl, vol.5, issue.9, pp.229-236, 1994. ,
Non fattening condition for the generalized evolution by mean curvature and applications. Interfaces Free Bound, pp.1-14, 2008. ,
Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions, Discrete and Continuous Dynamical Systems, vol.21, issue.3, pp.763-800, 2008. ,
DOI : 10.3934/dcds.2008.21.763
Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach, Discrete and Continuous Dynamical Systems, vol.21, issue.4, pp.1047-1069, 2008. ,
DOI : 10.3934/dcds.2008.21.1047
On front propagation problems with nonlocal terms, Adv. Differential Equations, vol.5, issue.1-3, pp.213-268, 2000. ,
On the approximation of front propagation problems with nonlocal terms, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.3, pp.437-462, 2001. ,
DOI : 10.1051/m2an:2001120
Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Journal of Differential Geometry, vol.33, issue.3, pp.749-786, 1991. ,
DOI : 10.4310/jdg/1214446564
Asymptotic behavior of solutions of an Allen-Cahn equation with a nonlocal term, Nonlinear Anal, pp.1283-1298, 1997. ,
Nonsmooth analysis and control theory, 1998. ,
DOI : 10.1007/978-1-4614-1806-1_69
URL : https://hal.archives-ouvertes.fr/hal-00863298
user's guide to viscosity solutions\\ of second order\\ partial
differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992. ,
DOI : 10.1090/S0273-0979-1992-00266-5
Nonlocal front propagation problems in bounded domains with Neumann-type boundary conditions and applications, Asymptot. Anal, vol.37, pp.3-4, 2004. ,
Measure theory and fine properties of functions, Studies in Advanced Mathematics, 1992. ,
Motion of level sets by mean curvature. I, J. Differential Geom, pp.635-681, 1991. ,
Regularity of the distance function, Proc. Amer, pp.153-155, 1984. ,
DOI : 10.1090/S0002-9939-1984-0749908-9
Minimizing movements for dislocation dynamics with a mean curvature term, ESAIM: Control, Optimisation and Calculus of Variations, vol.15, issue.1, pp.214-244, 2009. ,
DOI : 10.1051/cocv:2008027
URL : https://hal.archives-ouvertes.fr/hal-00149406
Surface evolution equations. A level set approach, Monographs in Mathematics, vol.99, 2006. ,
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
Sharp growth rate for generalized solutions evolving by mean curvature plus a forcing term, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2001, issue.538, pp.1-24, 2001. ,
DOI : 10.1515/crll.2001.065
Variation et optimisation de formes, 2005. ,
DOI : 10.1007/3-540-37689-5
Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Fac. Sci. Engrg. Chuo Univ, vol.28, pp.33-77, 1985. ,
Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Equations, Journal of Differential Equations, vol.183, issue.2, pp.497-525, 2002. ,
DOI : 10.1006/jdeq.2001.4136
Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations, Electron. J. Differential Equations, vol.10, issue.39, p.pp. (electronic), 2002. ,
A fattening principle for fronts propagating by mean curvature plus a driving force, Communications in Partial Differential Equations, vol.33, issue.5-6, pp.5-6, 1999. ,
DOI : 10.1016/0021-9991(88)90002-2
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. ,
Differentiable functions on bad domains, 1997. ,
Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence, Nonlinear Anal, pp.1033-1062, 1992. ,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
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
Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions, Nonlinear Anal, pp.79-115, 2003. ,
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
Nonlocal second-order Hamilton-Jacobi equations arising in tomographic reconstruction , Nonlinear Anal, TMA, vol.71, pp.1746-1762, 2009. ,