Completeness theorems on the boundary for a parabolic equation
Year: 2026
Type: preprint
Abstract: 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 $a_{hk}\partial_{x_{h}x_{k}} u+ \partial_t u =0$.
Source: arXiv (Cornell University)
Institution: University of Basilicata
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7130393259
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