Cyril Imbert

Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations

This paper is concerned with the Holder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth conditions on the equation. These results are concerned with a large class of integro-differential operators whose singular measures depend on x and also a large class of equations, including Bellman-Isaacs Equations.

Optimal Control under Stochastic Target Constraints

We study a class of Markovian optimal stochastic control problems in which the controlled process

Homogenization of First Order Equations with (u/ε)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics

Z^{\nu}

Asymptotic Properties of Entropy Solutions to Fractal Burgers Equation

is constrained to satisfy an almost sure constraint

A Kinetic Formulation for Multidimensional Scalar Conservation Laws with Boundary Conditions and Applications

Z^{\nu}(T)\in G\subset\mathbb{R}^{d+1}

Estimates on elliptic equations that hold only where the gradient is large

\mathbb{P}

Level set approach for fractional mean curvature flows

-a.s. at some final time

C1,a regularity of solutions of some degenerate fully non-linear elliptic equations

T>0

The Lévy–Fokker–Planck equation: Φ-entropies and convergence to equilibrium

. When the set is of the form