Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger inequalities on graded groups and ground states
- Author
- Michael Ruzhansky (UGent) and Nurgissa Yessirkegenov
- Organization
- Project
- Abstract
- In this paper, we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded Lie groups, which include the cases of R-n, Heisenberg, and general stratified Lie groups. As an application, using the critical Gagliardo-Nirenberg inequality, the existence of least energy solutions of nonlinear Schrodinger type equations is obtained. We also express the best constant in the critical Gagliardo-Nirenberg and Trudinger inequalities in the variational form as well as in terms of the ground state solutions of the corresponding nonlinear subelliptic equations. The obtained results are already new in the setting of general stratified Lie groups (homogeneous Carnot groups). Among new technical methods, we also extend Folland's analysis of Holder spaces from stratified Lie groups to general homogeneous Lie groups.
- Keywords
- Applied Mathematics, General Mathematics, Ghent Analysis & PDE center, Trudinger inequality, Gagliardo-Nirenberg inequality, Sobolev inequality, Rockland operator, graded Lie group, stratified Lie group, sub-Laplacian, SHARP MOSER-TRUDINGER, HEISENBERG-GROUP, WEAK SOLUTIONS, EQUATIONS, SPACES, EXISTENCE, PROOF
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01H2SYTG3C6VCQ60X0385Q3J7J
- MLA
- Ruzhansky, Michael, and Nurgissa Yessirkegenov. “Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger Inequalities on Graded Groups and Ground States.” COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 24, no. 08, 2022, doi:10.1142/s0219199721500619.
- APA
- Ruzhansky, M., & Yessirkegenov, N. (2022). Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger inequalities on graded groups and ground states. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 24(08). https://doi.org/10.1142/s0219199721500619
- Chicago author-date
- Ruzhansky, Michael, and Nurgissa Yessirkegenov. 2022. “Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger Inequalities on Graded Groups and Ground States.” COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 24 (08). https://doi.org/10.1142/s0219199721500619.
- Chicago author-date (all authors)
- Ruzhansky, Michael, and Nurgissa Yessirkegenov. 2022. “Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger Inequalities on Graded Groups and Ground States.” COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 24 (08). doi:10.1142/s0219199721500619.
- Vancouver
- 1.Ruzhansky M, Yessirkegenov N. Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger inequalities on graded groups and ground states. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. 2022;24(08).
- IEEE
- [1]M. Ruzhansky and N. Yessirkegenov, “Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger inequalities on graded groups and ground states,” COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 24, no. 08, 2022.
@article{01H2SYTG3C6VCQ60X0385Q3J7J,
abstract = {{In this paper, we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded Lie groups, which include the cases of R-n, Heisenberg, and general stratified Lie groups. As an application, using the critical Gagliardo-Nirenberg inequality, the existence of least energy solutions of nonlinear Schrodinger type equations is obtained. We also express the best constant in the critical Gagliardo-Nirenberg and Trudinger inequalities in the variational form as well as in terms of the ground state solutions of the corresponding nonlinear subelliptic equations. The obtained results are already new in the setting of general stratified Lie groups (homogeneous Carnot groups). Among new technical methods, we also extend Folland's analysis of Holder spaces from stratified Lie groups to general homogeneous Lie groups.}},
articleno = {{2150061}},
author = {{Ruzhansky, Michael and Yessirkegenov, Nurgissa}},
issn = {{0219-1997}},
journal = {{COMMUNICATIONS IN CONTEMPORARY MATHEMATICS}},
keywords = {{Applied Mathematics,General Mathematics,Ghent Analysis & PDE center,Trudinger inequality,Gagliardo-Nirenberg inequality,Sobolev inequality,Rockland operator,graded Lie group,stratified Lie group,sub-Laplacian,SHARP MOSER-TRUDINGER,HEISENBERG-GROUP,WEAK SOLUTIONS,EQUATIONS,SPACES,EXISTENCE,PROOF}},
language = {{eng}},
number = {{08}},
pages = {{29}},
title = {{Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger inequalities on graded groups and ground states}},
url = {{http://doi.org/10.1142/s0219199721500619}},
volume = {{24}},
year = {{2022}},
}
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