Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914946972909568 |
|---|---|
| author | Ikeda, Masahiro Sano, Megumi Taniguchi, Koichi |
| author_facet | Ikeda, Masahiro Sano, Megumi Taniguchi, Koichi |
| contents | We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces $\dot{W}^{1,p}_{0, \text{rad}}(B_R^N)\,(p<N)$. Our results give a revision of an error in \cite[Theorem C]{HL}. Also, our inequality converges to the original Trudinger-Moser inequality as $p \nearrow N$ including optimal exponent and concentration limit. Finally, we consider an application of our inequality to elliptic problems with exponential nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15274 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications Ikeda, Masahiro Sano, Megumi Taniguchi, Koichi Analysis of PDEs Functional Analysis We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces $\dot{W}^{1,p}_{0, \text{rad}}(B_R^N)\,(p<N)$. Our results give a revision of an error in \cite[Theorem C]{HL}. Also, our inequality converges to the original Trudinger-Moser inequality as $p \nearrow N$ including optimal exponent and concentration limit. Finally, we consider an application of our inequality to elliptic problems with exponential nonlinearity. |
| title | Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2401.15274 |