Displaying similar documents to “Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities”

Lieb–Thirring inequalities with improved constants

Jean Dolbeault, Ari Laptev, Michael Loss (2008)

Journal of the European Mathematical Society

Similarity:

Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb–Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrödinger operators.

A sharp iteration principle for higher-order Sobolev embeddings

Andrea Cianchi, Luboš Pick, Lenka Slavíková (2014)

Banach Center Publications

Similarity:

We survey results from the paper [CPS] in which we developed a new sharp iteration method and applied it to show that the optimal Sobolev embeddings of any order can be derived from isoperimetric inequalities. We prove thereby that the well-known link between first-order Sobolev embeddings and isoperimetric inequalities translates to embeddings of any order, a fact that had not been known before. We show a general reduction principle that reduces Sobolev type inequalities of any order...

Inequalities of DVT-type -- the one-dimensional case

Barbora Batíková, Tomáš J. Kepka, Petr C. Němec (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this note, particular inequalities of DVT-type in real and integer numbers are investigated.