Ground states for fractional magnetic operators

TL;DR

This paper investigates the mathematical properties of fractional magnetic operators, focusing on the existence of ground states through variational methods and concentration compactness techniques.

Contribution

It introduces a new class of minimization problems for nonlocal magnetic operators and establishes existence results under physically justified conditions.

Findings

Existence of ground state solutions proven

Solutions are consistent with non-magnetic cases

Methodology extends variational techniques to nonlocal magnetic operators

Abstract

We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration compactness.