The Sharp Sobolev Inequality and Its Stability: An Introduction
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.
Copyright and License
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
© 2023 by the author. This paper may be reproduced, in its entirety, for noncommercial purposes.
Funding
Partial support through US National Science Foundation grant DMS-1954995, as well as through the Deutsche Forschungsgemeinschaft through Germany’s Excellence Strategy EXC-2111-390814868 and through TRR 352—Project-ID 470903074 is acknowledged.
Additional details
Related works
- Describes
- Journal Article: https://rdcu.be/d7YMk (URL)
- Is new version of
- Discussion Paper: arXiv:2304.03115 (arXiv)
Funding
- National Science Foundation
- DMS-1954995
- Deutsche Forschungsgemeinschaft
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft
- 470903074
Caltech Custom Metadata
- Series Name
- Lecture Notes in Mathematics
- Series Volume or Issue Number
- 2348
- Publication Status
- Published