Sub-elliptic boundary value problems in flag domains
| Autor: | Tuomas Orponen, Michele Villa |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Functional Analysis
Mathematics - Analysis of PDEs Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs Applied Mathematics Classical Analysis and ODEs (math.CA) FOS: Mathematics Metric Geometry (math.MG) 35R03 (Primary) 31E05 35H20 35S15 42B20 (Secondary) Analysis Analysis of PDEs (math.AP) Functional Analysis (math.FA) |
| Zdroj: | Advances in Calculus of Variations. |
| ISSN: | 1864-8266 1864-8258 |
| DOI: | 10.1515/acv-2021-0077 |
| Popis: | A flag domain in $\mathbb{R}^{3}$ is a subset of $\mathbb{R}^{3}$ of the form $\{(x,y,t) : y < A(x)\}$, where $A \colon \mathbb{R} \to \mathbb{R}$ is a Lipschitz function. We solve the Dirichlet and Neumann problems for the sub-elliptic Kohn-Laplacian $\bigtriangleup^{\flat} = X^{2} + Y^{2}$ in flag domains $\Omega \subset \mathbb{R}^{3}$, with $L^{2}$-boundary values. We also obtain improved regularity for solutions to the Dirichlet problem if the boundary values have first order $L^{2}$-Sobolev regularity. Our solutions are obtained as sub-elliptic single and double layer potentials, which are best viewed as integral operators on the first Heisenberg group. We develop the theory of these operators on flag domains, and their boundaries. Comment: 95 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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