Lp-Liouville Property for Non-Local Operators
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2011
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916567557603328 |
|---|---|
| author | Masamune, Jun Uemura, Toshihiro |
| author_facet | Masamune, Jun Uemura, Toshihiro |
| contents | The Lp-Liouville property of a non-local operator A is investigated via the associated Dirichlet form. We will show that any non-negative continuous Lp E-subharmonic functions are constant under a quite mild assumption on the kernel of E if p is not less than 2. On the contrary, if 1 < p < 2, we need an additional assumption: either, the kernel has compact support; or f is Holder continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1103_1781 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Lp-Liouville Property for Non-Local Operators Masamune, Jun Uemura, Toshihiro Analysis of PDEs Probability 42B20 (Primary), 47G20 (Secondary), 31B05, 31C25 The Lp-Liouville property of a non-local operator A is investigated via the associated Dirichlet form. We will show that any non-negative continuous Lp E-subharmonic functions are constant under a quite mild assumption on the kernel of E if p is not less than 2. On the contrary, if 1 < p < 2, we need an additional assumption: either, the kernel has compact support; or f is Holder continuous. |
| title | Lp-Liouville Property for Non-Local Operators |
| topic | Analysis of PDEs Probability 42B20 (Primary), 47G20 (Secondary), 31B05, 31C25 |
| url | https://arxiv.org/abs/1103.1781 |