Characterization of the weighted Sobolev space $H_β^{s}(Ω)$ in $\mathbb{R}^{2}$ in terms of the decay rate of Fourier-Jacobi coefficients
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914743413899264 |
|---|---|
| author | Ervin, V. J. |
| author_facet | Ervin, V. J. |
| contents | In this paper, motivated by the analysis of the fractional Laplace equation on the unit disk in $\mathbb{R}^{2}$, we establish a characterization of the weighted Sobolev space $H_β^{s}(Ω)$ in terms of the decay rate of Fourier-Jacobi coefficients. This framework is then used to give a precise analysis of the solution to the fractional Laplace equation on the unit disk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04658 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of the weighted Sobolev space $H_β^{s}(Ω)$ in $\mathbb{R}^{2}$ in terms of the decay rate of Fourier-Jacobi coefficients Ervin, V. J. Analysis of PDEs 33C45, 33C55, 35A09, 60K50 In this paper, motivated by the analysis of the fractional Laplace equation on the unit disk in $\mathbb{R}^{2}$, we establish a characterization of the weighted Sobolev space $H_β^{s}(Ω)$ in terms of the decay rate of Fourier-Jacobi coefficients. This framework is then used to give a precise analysis of the solution to the fractional Laplace equation on the unit disk. |
| title | Characterization of the weighted Sobolev space $H_β^{s}(Ω)$ in $\mathbb{R}^{2}$ in terms of the decay rate of Fourier-Jacobi coefficients |
| topic | Analysis of PDEs 33C45, 33C55, 35A09, 60K50 |
| url | https://arxiv.org/abs/2404.04658 |