On mixed local-nonlocal problems with Hardy potential

In this paper we study the effect of the Hardy potential on existence, uniqueness and optimal summability of solutions of the mixed local-nonlocal elliptic problem -Δ u + (-Δ)ˢ u - γ u/|x|²=f in Ω, \ u=0 in Rⁿ Ω, where Ω is a bounded domain in Rⁿ 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.