The sharp Sobolev inequality and its stability: An introduction
Analysis of PDEs
2023-04-25 v2 Differential Geometry
Functional Analysis
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.
Cite
@article{arxiv.2304.03115,
title = {The sharp Sobolev inequality and its stability: An introduction},
author = {Rupert L. Frank},
journal= {arXiv preprint arXiv:2304.03115},
year = {2023}
}
Comments
52 pages; lecture notes from a course held at the CIME Summer School in June 2022; minor changes in v2