Regularity results on a class of doubly nonlocal problems

TL;DR

This paper studies the regularity of solutions to a class of doubly nonlocal problems and explores the relationship between different types of minimizers, providing applications to existence and multiplicity of solutions.

Contribution

It establishes regularity results for weak solutions and compares $H^s$ and $C^0$-weighted minimizers, advancing understanding of solution properties in nonlocal problems.

Findings

Regularity of weak solutions is established.

Comparison between $H^s$ and $C^0$-weighted minimizers is analyzed.

Applications to existence and multiplicity of solutions are provided.

Abstract

The purpose of this article is twofold. First, an issue of regularity of weak solution to the problem $(P)$ (See below) is addressed. Secondly, we investigate the question of $H^s$ versus $C^0$- weighted minimizers of the functional associated to problem $(P)$ and then give applications to existence and multiplicity results.