Optimal decay of extremals for the fractional Sobolev inequality

TL;DR

This paper characterizes the precise asymptotic decay of extremal functions associated with the fractional Sobolev inequality, providing insights into their behavior at infinity.

Contribution

It establishes the exact decay rates of extremal functions for the fractional critical Sobolev embedding, advancing understanding of their asymptotic properties.

Findings

Determined the sharp decay rate of extremals at infinity.

Provided explicit asymptotic formulas for extremal functions.

Enhanced understanding of fractional Sobolev inequalities.

Abstract

We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding.