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Limiting cases of Sobolev inequalities on stratified groups

Michael Ruzhansky (UGent) and Nurgissa Yessirkegenov (UGent)
(2019) PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES. 95(8). p.83-87
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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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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://dx.doi.org/10.3792/pjaa.95.83}},
  volume       = {{95}},
  year         = {{2019}},
}
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