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 $u\in W^{2,p}(\mathrm{\Omega })$ of the considered problem with $L^p$-source function when $p$ and $s$ are in a certain range.