Semilinear fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions

Abstract

We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed Dirichlet-Neumann boundary conditions.

Regularity of solutions to a fractional elliptic problem with mixed Dirichlet–Neumann boundary data

“…Let us stress that problem related to the spectral fractional Laplacian with mixed boundary conditions are news and, to our knowledge, have been treated only in [4,5].…”