On mixed local–nonlocal problems with Hardy potential

Abstract In this article, we study the effect of the Hardy potential on existence, uniqueness, and optimal summability of solutions of the mixed local–nonlocal elliptic problem \begin{equation*}-\Delta u + (-\Delta)^s u - \gamma \frac{u}{|x|^2}=f \,\text{in } \Omega, \ u=0 \,\text{in } {\mathbb R}^n \setminus \Omega,\end{equation*} where Ω is a bounded domain in ${\mathbb R}^n$ containing the origin and γ > 0. In particular, we will discuss the existence, non-existence, and uniqueness of solutions in terms of the summability of f and of the value of the parameter γ .