Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.07561 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916516909285376 |
|---|---|
| author | Li, Hai Wu, Longyu Zhu, Baocheng |
| author_facet | Li, Hai Wu, Longyu Zhu, Baocheng |
| contents | In this paper, we consider an extremal problem associated with the solution to a boundary value problem. Our main focus is on establishing a variational formula for a functional related to the $\mathbf{p}$-harmonic measure, from which a new measure is derived. This further motivates us to study the Minkowski problem for this new measure. As a main result, we prove the existence of solutions to the $L_q$ Minkowski problem associated with the $\mathbf{p}$-harmonic measure for $0<q<1$ and $1<\mathbf{p}\ne n+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $L_q$ Minkowski problem for $\mathbf{p}$-harmonic measure Li, Hai Wu, Longyu Zhu, Baocheng Analysis of PDEs In this paper, we consider an extremal problem associated with the solution to a boundary value problem. Our main focus is on establishing a variational formula for a functional related to the $\mathbf{p}$-harmonic measure, from which a new measure is derived. This further motivates us to study the Minkowski problem for this new measure. As a main result, we prove the existence of solutions to the $L_q$ Minkowski problem associated with the $\mathbf{p}$-harmonic measure for $0<q<1$ and $1<\mathbf{p}\ne n+1$. |
| title | The $L_q$ Minkowski problem for $\mathbf{p}$-harmonic measure |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.07561 |