The aim of this work is to revisit viscosity solutions’ theory for second-order elliptic integrodifferential equations and to provide a general framework which takes into account solutions with… (More)

In this article, we consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, which consists in imposing the “boundary conditions” in the whole… (More)

The present paper is concerned with semilinear partial differential equations involving a particular pseudo-differential operator. It investigates both fractal conservation laws and non-local… (More)

This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set. Moreover the… (More)

The starting point of this work is a paper by Alvarez, Lasry and Lions (1997) concerning the convexity and the partial convexity of solutions of fully nonlinear degenerate elliptic equations. We… (More)

In this paper, we present a result of homogenization of first order Hamilton-Jacobi equations with (u/ε)-periodic Hamiltonians. On the one hand, under a coercivity assumption on the Hamiltonian (and… (More)

We study a class of Markovian optimal stochastic control problems in which the controlled process Z is constrained to satisfy an a.s. constraint Z(T ) ∈ G ⊂ R P − a.s. at some final time T > 0. When… (More)

This paper is devoted to the study of semi-linear parabolic equations whose principal term is fractional, i.e. is integral and eventually singular. A typical example is the fractional Laplace… (More)

This paper is concerned with the homogenization of a non-local first order Hamilton-Jacobi equation describing the dynamics of several dislocation lines and the homogenization of some particle… (More)

In this paper, we study a Fokker-Planck equation of the form ut = I[u] + div(xu) where the operator I, which is usually the Laplacian, is replaced here with a general Lévy operator. We prove by the… (More)