Extremal functions for a fractional Morrey inequality: Symmetry properties and limit at infinity

TL;DR

This paper investigates extremal functions for a fractional Morrey inequality, focusing on their symmetry properties and behavior at infinity, extending previous work on classical Morrey inequalities to fractional Sobolev spaces.

Contribution

It extends the analysis of extremal functions to fractional Sobolev spaces, confirming symmetry and asymptotic properties analogous to classical cases.

Findings

Extremals exhibit symmetry properties similar to classical Morrey extremals.

The limit behavior of extremals at infinity is characterized.

Results build upon and verify previous findings in the fractional setting.

Abstract

In a series of articles, Ryan Hynd and Francis Seuffert have studied extremal functions for the Morrey inequality. Building upon their work, we study the extremals of a Morrey-type inequality for fractional Sobolev spaces. We verify a few of the results in the spirit of Hynd and Seuffert concerning the symmetry of extremals and their limit at infinity.