The sharp Sobolev inequality and its stability: An introduction

2023/04/06 by Rupert L. Frank, Frank, Rupert L. · 6 citations
Engineering · #Fatigue and fracture mechanics

paper · pdf · doi:10.48550/arxiv.2304.03115

Abstract

These notes are an extended version of a series of lectures given at the CIME Summer School in Cetraro in June 2022. The goal is to explain questions about optimal functional inequalities on the example of the sharp Sobolev inequality and its fractional generalizations. Topics covered include compactness theorems for optimizing sequences, characterization of optimizers and quantitative stability.

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