Regularity results for Choquard equations involving fractional p‐Laplacian

Abstract

AbstractIn this paper, first we address the regularity of weak solution for a class of p‐fractional Choquard equations: where is a smooth bounded domain, and such that , and is a continuous function with at most critical growth condition (in the sense of the Hardy–Littlewood–Sobolev inequality) and F is its primitive. Next, for , we discuss the Sobolev versus Hölder minimizers of the energy functional J associated with the above problem, and using that we establish the existence of the local minimizer of J in the fractional Sobolev space . Moreover, we discuss the aforementioned results by adding a local perturbation term (at most critical in the sense of Sobolev inequality) in the right‐hand side in the above equation.