Gradient estimates in fractional Dirichlet problems

TL;DR

This paper derives precise gradient estimates near the boundary for solutions to fractional elliptic problems with Dirichlet conditions, revealing the sign of the normal derivative close to the boundary.

Contribution

It provides new boundary gradient estimates and determines the sign of the normal derivative for fractional elliptic solutions.

Findings

Gradient estimates near the boundary for fractional elliptic solutions.

Sign of the normal derivative determined near the boundary.

Enhanced understanding of boundary behavior in fractional PDEs.

Abstract

We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such solutions near the boundary of the underlying domain.