Existence and regularity results for a Neumann problem with mixed local and nonlocal diffusion

In this paper, we consider an elliptic problem driven by a mixed local-nonlocal operator with drift and subject to nonlocal Neumann condition. We prove the existence and uniqueness of a solution u∈ W2,p(Ω) of the considered problem with Lᵖ-source function when p and s are in a certain range.