Fully nonlinear integro-differential equations with deforming kernels

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...

Integro-differential Equations with Nonlinear Directional Dependence

We prove Hölder regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also uniform as the order of operators approaches 2.

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...