$$W^{\sigma ,p}$$ A priori estimates for fully nonlinear integro-differential equations

Regularity theory for fully nonlinear integro-differential equations

We consider nonlinear integro-differential equations like the ones that arise from stochastic control problems with purely jump Lévy processes. We obtain a nonlocal version of the ABP estimate, Harnack inequality, and interior C 1; ̨ regularity for general fully nonlinear integro-differential equations. Our estimates remain uniform as the degree of the equation approaches 2, so they can be seen ...

Boundary Regularity for Fully Nonlinear Integro-differential Equations

We study fine boundary regularity properties of solutions to fully nonlinear elliptic integro-differential equations of order 2s, with s 2 .0; 1/. We consider the class of nonlocal operators L L0, which consists of infinitesimal generators of stable Lévy processes belonging to the class L0 of Caffarelli–Silvestre. For fully nonlinear operators I elliptic with respect to L , we prove that soluti...

Nonlinear Integro - Differential Equations

Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

A Priori Estimates and Existence for a Class of Fully Nonlinear Elliptic Equations in Conformal Geometry

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive. Dedicated to the memory of Profess...