Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.20121 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916810701406208 |
|---|---|
| author | Lee, David |
| author_facet | Lee, David |
| contents | Existence of the fundamental solution of the logarithmic Laplacian (in dimensions $d \geq 3$) was established by Huyuan Chen and Laurent Véron (2024). In this note, we present an alternative approach, based on a modification on the classical division problem. This is inspired by the theory of fundamental solutions by Malgrange and Ehrenpreis. Moreover, we give a variant of the Liouville theorem for the logarithmic Laplacian and give some further clarification regarding a conjecture posed by Chen and Véron regarding the behavior of solutions in dimensions 1 and 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem Lee, David Analysis of PDEs 42B37, 42B15, 46F10 Existence of the fundamental solution of the logarithmic Laplacian (in dimensions $d \geq 3$) was established by Huyuan Chen and Laurent Véron (2024). In this note, we present an alternative approach, based on a modification on the classical division problem. This is inspired by the theory of fundamental solutions by Malgrange and Ehrenpreis. Moreover, we give a variant of the Liouville theorem for the logarithmic Laplacian and give some further clarification regarding a conjecture posed by Chen and Véron regarding the behavior of solutions in dimensions 1 and 2. |
| title | Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem |
| topic | Analysis of PDEs 42B37, 42B15, 46F10 |
| url | https://arxiv.org/abs/2506.20121 |