$L_p$-estimates for nonlocal equations with general Lévy measures
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909978987593728 |
|---|---|
| author | Dong, Hongjie Ryu, Junhee |
| author_facet | Dong, Hongjie Ryu, Junhee |
| contents | We consider nonlocal operators of the form \begin{equation*}
L_t u(x) = \int_{\mathbb{R}^d} \left( u(x+y)-u(x)-\nabla u(x)\cdot y^{(σ)} \right) ν_t(dy), \end{equation*} where $ν_t$ is a general Lévy measure of order $σ\in(0,2)$. We allow this class of Lévy measures to be very singular and impose no regularity assumptions in the time variable. Continuity of the operators and the unique strong solvability of the corresponding nonlocal parabolic equations in $L_p$ spaces are established. We also demonstrate that, depending on the ranges of $σ$ and $d$, the operator can or cannot be treated in weighted mixed-norm spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L_p$-estimates for nonlocal equations with general Lévy measures Dong, Hongjie Ryu, Junhee Analysis of PDEs 35B65, 35R11, 45K05, 47G20 We consider nonlocal operators of the form \begin{equation*} L_t u(x) = \int_{\mathbb{R}^d} \left( u(x+y)-u(x)-\nabla u(x)\cdot y^{(σ)} \right) ν_t(dy), \end{equation*} where $ν_t$ is a general Lévy measure of order $σ\in(0,2)$. We allow this class of Lévy measures to be very singular and impose no regularity assumptions in the time variable. Continuity of the operators and the unique strong solvability of the corresponding nonlocal parabolic equations in $L_p$ spaces are established. We also demonstrate that, depending on the ranges of $σ$ and $d$, the operator can or cannot be treated in weighted mixed-norm spaces. |
| title | $L_p$-estimates for nonlocal equations with general Lévy measures |
| topic | Analysis of PDEs 35B65, 35R11, 45K05, 47G20 |
| url | https://arxiv.org/abs/2512.24704 |