Open Access
October 2019 Limiting cases of Sobolev inequalities on stratified groups
Michael Ruzhansky, Nurgissa Yessirkegenov
Proc. Japan Acad. Ser. A Math. Sci. 95(8): 83-87 (October 2019). DOI: 10.3792/pjaa.95.83


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.


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Michael Ruzhansky. Nurgissa Yessirkegenov. "Limiting cases of Sobolev inequalities on stratified groups." Proc. Japan Acad. Ser. A Math. Sci. 95 (8) 83 - 87, October 2019.


Published: October 2019
First available in Project Euclid: 2 October 2019

zbMATH: 07213564
MathSciNet: MR4014782
Digital Object Identifier: 10.3792/pjaa.95.83

Primary: 35G20 , 35J35
Secondary: 22E30 , 43A80

Keywords: Gagliardo-Nirenberg inequality , Sobolev inequality , stratified group , sub-Laplacian , Trudinger inequality

Rights: Copyright © 2019 The Japan Academy

Vol.95 • No. 8 • October 2019
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