Optimal geometric estimates for fractional Sobolev capacities

2014/04/08 by Xiao, Jie
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.2245

Abstract

This note develops certain sharp inequalities relating the fractional Sobolev capacity of a set to its standard volume and fractional perimeter.

Related

• Characterizations to the fractional Sobolev inequality
• Limit of Fractional Power Sobolev Inequalities
• Volume constrained minimizers of the fractional perimeter with a potential energy
• Sharp Fractional Sobolev Embeddings on Closed Manifolds
• Minimizers for the fractional Sobolev inequality on domains