
Limiting cases of Sobolev inequalities on stratified groups
- Author
- Michael Ruzhansky (UGent) and Nurgissa Yessirkegenov (UGent)
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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.
- Keywords
- Trudinger inequality, Gagliardo-Nirenberg inequality, Sobolev inequality, stratified group, sub-Laplacian, MOSER-TRUDINGER INEQUALITIES, WEAK SOLUTIONS, EQUATIONS, SPACES, PROOF
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8636232
- MLA
- Ruzhansky, Michael, and Nurgissa Yessirkegenov. “Limiting Cases of Sobolev Inequalities on Stratified Groups.” PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, vol. 95, no. 8, 2019, pp. 83–87, doi:10.3792/pjaa.95.83.
- APA
- Ruzhansky, M., & Yessirkegenov, N. (2019). Limiting cases of Sobolev inequalities on stratified groups. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 95(8), 83–87. https://doi.org/10.3792/pjaa.95.83
- Chicago author-date
- Ruzhansky, Michael, and Nurgissa Yessirkegenov. 2019. “Limiting Cases of Sobolev Inequalities on Stratified Groups.” PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 95 (8): 83–87. https://doi.org/10.3792/pjaa.95.83.
- Chicago author-date (all authors)
- Ruzhansky, Michael, and Nurgissa Yessirkegenov. 2019. “Limiting Cases of Sobolev Inequalities on Stratified Groups.” PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 95 (8): 83–87. doi:10.3792/pjaa.95.83.
- Vancouver
- 1.Ruzhansky M, Yessirkegenov N. Limiting cases of Sobolev inequalities on stratified groups. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES. 2019;95(8):83–7.
- IEEE
- [1]M. Ruzhansky and N. Yessirkegenov, “Limiting cases of Sobolev inequalities on stratified groups,” PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, vol. 95, no. 8, pp. 83–87, 2019.
@article{8636232, 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.}}, author = {{Ruzhansky, Michael and Yessirkegenov, Nurgissa}}, issn = {{0386-2194}}, journal = {{PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES}}, keywords = {{Trudinger inequality,Gagliardo-Nirenberg inequality,Sobolev inequality,stratified group,sub-Laplacian,MOSER-TRUDINGER INEQUALITIES,WEAK SOLUTIONS,EQUATIONS,SPACES,PROOF}}, language = {{eng}}, number = {{8}}, pages = {{83--87}}, title = {{Limiting cases of Sobolev inequalities on stratified groups}}, url = {{http://doi.org/10.3792/pjaa.95.83}}, volume = {{95}}, year = {{2019}}, }
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