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Limiting cases of Sobolev inequalities on stratified groups

Authors
  • Ruzhansky, Michael
  • Yessirkegenov, Nurgissa
Publication Date
Jan 01, 2019
Source
Ghent University Institutional Archive
Keywords
Language
English
License
Unknown
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Abstract

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 Schrodinger 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.

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