Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.15621 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914334367547392 |
|---|---|
| author | Cialdea, Alberto Mare, Carmine Sebastiano |
| author_facet | Cialdea, Alberto Mare, Carmine Sebastiano |
| contents | Let $\{v_α\}$ be a system of polynomial solutions of the parabolic equation $a_{hk}\partial_{x_{h}x_{k}}u - \partial_t u =0$ in a bounded $C^1$-cylinder $Ω_{T}$ contained in $\mathbb{R}^{n+1}$. Here $a_{hk}\partial_{x_{h}x_{k}}$ is an elliptic operator with real constant coefficients. We prove that $\{v_α\}$ is complete in $L^{p}(Σ')$, where $Σ'$ is the parabolic boundary of $Ω_{T}$. Similar results are proved for the adjoint equation $a_{hk}\partial_{x_{h}x_{k}} u+ \partial_t u =0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Completeness theorems on the boundary for a parabolic equation Cialdea, Alberto Mare, Carmine Sebastiano Analysis of PDEs 42C30, 35K20, 35A35 Let $\{v_α\}$ be a system of polynomial solutions of the parabolic equation $a_{hk}\partial_{x_{h}x_{k}}u - \partial_t u =0$ in a bounded $C^1$-cylinder $Ω_{T}$ contained in $\mathbb{R}^{n+1}$. Here $a_{hk}\partial_{x_{h}x_{k}}$ is an elliptic operator with real constant coefficients. We prove that $\{v_α\}$ is complete in $L^{p}(Σ')$, where $Σ'$ is the parabolic boundary of $Ω_{T}$. Similar results are proved for the adjoint equation $a_{hk}\partial_{x_{h}x_{k}} u+ \partial_t u =0$. |
| title | Completeness theorems on the boundary for a parabolic equation |
| topic | Analysis of PDEs 42C30, 35K20, 35A35 |
| url | https://arxiv.org/abs/2602.15621 |