On the Dirichlet problem for fractional Laplace equation on a general domain
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929628401106944 |
|---|---|
| author | Liu, Chenkai Zhuo, Ran |
| author_facet | Liu, Chenkai Zhuo, Ran |
| contents | In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and Poisson kernels are important tools needed in our study. We first establish the existence of Green's function by an application of Perron's method. After that, the Poisson kernel is constructed based on the Green's function. Several important properties of Green's functions and Poisson kernels are proved. Finally, we show that the solution of a fractional Laplace (Poisson) equation under a given condition must be unique and be given by our Green's function and Poisson kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12546 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Dirichlet problem for fractional Laplace equation on a general domain Liu, Chenkai Zhuo, Ran Analysis of PDEs 35A01, 35B45, 35J08, 35S05 In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and Poisson kernels are important tools needed in our study. We first establish the existence of Green's function by an application of Perron's method. After that, the Poisson kernel is constructed based on the Green's function. Several important properties of Green's functions and Poisson kernels are proved. Finally, we show that the solution of a fractional Laplace (Poisson) equation under a given condition must be unique and be given by our Green's function and Poisson kernel. |
| title | On the Dirichlet problem for fractional Laplace equation on a general domain |
| topic | Analysis of PDEs 35A01, 35B45, 35J08, 35S05 |
| url | https://arxiv.org/abs/2206.12546 |