## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Limiting cases of Sobolev inequalities on stratified groups

#### 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 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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 95, Number 8 (2019), 83-87.

Dates
First available in Project Euclid: 2 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.pja/1570003225

Digital Object Identifier
doi:10.3792/pjaa.95.83

Mathematical Reviews number (MathSciNet)
MR4014782

#### Citation

Ruzhansky, Michael; Yessirkegenov, Nurgissa. Limiting cases of Sobolev inequalities on stratified groups. Proc. Japan Acad. Ser. A Math. Sci. 95 (2019), no. 8, 83--87. doi:10.3792/pjaa.95.83. https://projecteuclid.org/euclid.pja/1570003225

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