A Characterization of Solvability of the Parabolic $L^p$ Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908520136310784 |
|---|---|
| author | Warta, James Hofmann, Steve |
| author_facet | Warta, James Hofmann, Steve |
| contents | In this paper, we show that if the bounded solutions to the parabolic Dirichlet problem on a Lipshitz-$\left[1,\frac{1}{2}\right]$ domain obey a Carleson measure estimate, then the corresponding parabolic measure on the boundary will belong to class $A^\infty$, which is equivalent to $L^p$ solvability for some $p<\infty$. This improves the existing literature which places additional assumptions on the parabolic uniform rectifiability or, equivalently, on the half-order time derivative of the function whose graph defines the boundary of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Characterization of Solvability of the Parabolic $L^p$ Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions Warta, James Hofmann, Steve Analysis of PDEs 35A01 In this paper, we show that if the bounded solutions to the parabolic Dirichlet problem on a Lipshitz-$\left[1,\frac{1}{2}\right]$ domain obey a Carleson measure estimate, then the corresponding parabolic measure on the boundary will belong to class $A^\infty$, which is equivalent to $L^p$ solvability for some $p<\infty$. This improves the existing literature which places additional assumptions on the parabolic uniform rectifiability or, equivalently, on the half-order time derivative of the function whose graph defines the boundary of the domain. |
| title | A Characterization of Solvability of the Parabolic $L^p$ Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions |
| topic | Analysis of PDEs 35A01 |
| url | https://arxiv.org/abs/2509.04701 |