Increase the visibility of your scientific production by authorizing the export of your publications to HAL!

The limiting {S}obolev-{D}irac inequality

Schindler, Ian and Tintarev, Cyril (2013) The limiting {S}obolev-{D}irac inequality. Rostocker Mathematisches Kolloquium (n° 68).

 Preview
Text

Abstract

We prove the critical Dirac-Sobolev inequality for $p\in(1,3)$.
It follows that the Dirac Sobolev spaces are equivalent to classical
Sobolev spaces if and only if $p\in(1,3)$. We prove the cocompactness
of $L^{p^{*}}(\mathbb{R}^{3})$ in }{\normalsize{$\dot{\mathbf{H}}^{1,p}(\mathbb{R}^{3})$.
As an application, we prove the existence of minimizers to a class
of isoperimetric problems.

Item Type: Article English 2013 Yes G- MATHEMATIQUES Institut de mathématiques de Toulouse, TSE-R (Toulouse) UT1 08 Mar 2018 14:40 26 Feb 2020 15:49 http://publications.ut-capitole.fr/id/eprint/25107