Limiting cases of Sobolev inequalities on stratified groups

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Michael Ruzhansky¹  Nurgissa Yessirkegenov³ 

[1] Department of Mathematics: Analysis, Ghent University;School of Mathematical Sciences, Queen Mary University of London, United Kingdom.;Institute of Mathematics and Mathematical Modelling;Department of Mathematics, Imperial College London, United Kingdom.

关键词: Trudinger inequality;    Gagliardo-Nirenberg inequality;    Sobolev inequality;    stratified group;    sub-Laplacian.;   

DOI  :  10.3792/pjaa.95.83

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

In this paper we present critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities concerning the limiting cases of the embedding theorems for Sobolev spaces on stratified groups. Moreover, using the critical Gagliardo-Nirenberg inequality the existence of least energy solutions of the nonlinear Schrödinger type equations can be obtained. We also express the best constant in the critical Gagliardo-Nirenberg inequality in the variational form as well as in terms of the ground state solutions of the corresponding nonlinear subelliptic equations.

【 授权许可】

Unknown