Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions

Abstract

The Marchaud fractional derivative can be obtained as a Dirichlet-to–Neumann map via an extension problem to the upper half space. In this paper we prove interior Schauder regularity estimates for a degenerate elliptic equation with mixed Dirichlet–Neumann boundary conditions. The degenerate elliptic equation arises from the Bernardis–Reyes–Stinga–Torrea extension of the Dirichlet problem for the Marchaud fractional derivative.

Keywords

• marchaud fractional derivative
• interior regularity
• schauder estimate
• extension problem
• fractional order weighted Sobolev spaces