A representation formula for the distributional normal derivative
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912219871051776 |
|---|---|
| author | Ponce, Augusto C. Wilmet, Nicolas |
| author_facet | Ponce, Augusto C. Wilmet, Nicolas |
| contents | We prove an integral representation formula for the distributional normal derivative of solutions of $$ \left\{ \begin{aligned} - Δu + V u &= μ&& \text{in $Ω$,}\\ u &= 0 && \text{on $\partialΩ$,} \end{aligned} \right. $$ where $V \in L_{\mathrm{loc}}^1(Ω)$ is a nonnegative function and $μ$ is a finite Borel measure on $Ω$. As an application, we show that the Hopf lemma holds almost everywhere on $\partialΩ$ when $V$ is a nonnegative Hopf potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_02977 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A representation formula for the distributional normal derivative Ponce, Augusto C. Wilmet, Nicolas Analysis of PDEs 35J10, 31B10, 35B50 We prove an integral representation formula for the distributional normal derivative of solutions of $$ \left\{ \begin{aligned} - Δu + V u &= μ&& \text{in $Ω$,}\\ u &= 0 && \text{on $\partialΩ$,} \end{aligned} \right. $$ where $V \in L_{\mathrm{loc}}^1(Ω)$ is a nonnegative function and $μ$ is a finite Borel measure on $Ω$. As an application, we show that the Hopf lemma holds almost everywhere on $\partialΩ$ when $V$ is a nonnegative Hopf potential. |
| title | A representation formula for the distributional normal derivative |
| topic | Analysis of PDEs 35J10, 31B10, 35B50 |
| url | https://arxiv.org/abs/2009.02977 |