Minimality and Stability Properties in Sobolev and Isoperimetric Inequalities
Author | : Robin Tonra Neumayer |
Publisher | : |
Total Pages | : 400 |
Release | : 2017 |
ISBN-10 | : OCLC:1023039336 |
ISBN-13 | : |
Rating | : 4/5 (36 Downloads) |
Download or read book Minimality and Stability Properties in Sobolev and Isoperimetric Inequalities written by Robin Tonra Neumayer and published by . This book was released on 2017 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis addresses the characterization of minimizers in various Sobolev- and isoperimetric-type inequalities and the analysis of the corresponding stability phenomena. We first investigate a family of variational problems which arise in connection to a suitable interpolation between the classical Sobolev and Sobolev trace inequalities. We provide a full characterization of minimizers for each problem, in turn deriving a new family of sharp constrained Sobolev inequalities on the half-space. We then prove novel stability results for the Sobolev inequality and for the anisotropic isoperimetric inequality. Both of these results share the feature of being “strong-form” stability results, in the sense that the deficit in the inequality is shown to control the strongest possible distance to the family of equality cases.