Proceedings of the Japan Academy, Series A, Mathematical Sciences

Limiting cases of Sobolev inequalities on stratified groups

Michael Ruzhansky and Nurgissa Yessirkegenov

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

First available in Project Euclid: 2 October 2019

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Mathematical Reviews number (MathSciNet)

Primary: 35J35: Variational methods for higher-order elliptic equations 35G20: Nonlinear higher-order equations
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX] 43A80: Analysis on other specific Lie groups [See also 22Exx]

Trudinger inequality Gagliardo-Nirenberg inequality Sobolev inequality stratified group sub-Laplacian


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.

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