$W^{\sigma ,p}$ A Priori Estimates for Fully Nonlinear Integro-Differential Equations

Abstract

$W^{\sigma ,p}$ estimates are studied for a class of fully nonlinear integro-differential equations of order $\sigma$, which are analogues of $W^{2,p}$ estimates by Caffarelli. We also present Aleksandrov-Bakelman-Pucci maximum principles, which are improvements of estimates proved by Guillen-Schwab, depending only on $L^p$ norms of inhomogeneous terms.

References in corpus (1)

• ABP maximum principles for fully nonlinear integro-differential equations with unbounded inhomogeneous terms