Sharp affine Sobolev type inequalities via the $\Lp$ Busemann-Petty centroid inequality

By J. Haddad, C. H. Jiménez, Marcos Montenegro. 2015

69 citations recorded by the source corpus.

We show that the $\Lp$ Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo-Nirenberg inequalities. Our approach allows also to characterize directly the corresponding equality cases.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/424a53d3bca36aaf6aa3f91953de1b9db4f6f9c2