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

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.