Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.06390 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915434925654016 |
|---|---|
| author | Karlsen, Kenneth H. Petitta, Francesco Ulusoy, Suleyman |
| author_facet | Karlsen, Kenneth H. Petitta, Francesco Ulusoy, Suleyman |
| contents | We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like $$ (-Δ)^s v = μ\quad \text{in}\ \mathbb{R}^N, $$ with vanishing conditions at infinity.
Here $μ$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(Δ)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A duality approach to the fractional Laplacian with measure data Karlsen, Kenneth H. Petitta, Francesco Ulusoy, Suleyman Analysis of PDEs We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like $$ (-Δ)^s v = μ\quad \text{in}\ \mathbb{R}^N, $$ with vanishing conditions at infinity. Here $μ$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(Δ)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$. |
| title | A duality approach to the fractional Laplacian with measure data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.06390 |