On mixed local-nonlocal operators with (α, β)-Neumann conditions

Abstract

We consider some problems governed by the sum of a Laplacian and of a fractional Laplacian in presence of so–called (훼, 훽)-Neumann conditions in an essentially linear context. Indeed, frst we show an existence result for asymptotically linear elliptic problems, and then we establish some qualitative properties for solutions of the associated homogeneous parabolic problem, extending to this setting related results in the local case.