Spacelike graphs with prescribed mean curvature on exterior domains in the Minkowski spacetime
| Autor: | Erasmo Caponio, Alessio Pomponio, Rossella Bartolo |
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| Rok vydání: | 2020 |
| Předmět: |
Dirichlet problem
spacelike graphs 35J93 53C50 Pure mathematics Mean curvature Applied Mathematics General Mathematics Graph of a function mean curvature Absolute value (algebra) Minkowski spacetime Lipschitz continuity exterior domain Mathematics - Analysis of PDEs Bounded function Minkowski space FOS: Mathematics Mathematics::Differential Geometry Minkowski spacetime mean curvature spacelike graphs exterior domain Dirichlet problem Finite set Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2006.15116 |
| Popis: | We consider a Dirichlet problem for the mean curvature operator in the Minkowski spacetime, obtaining a necessary and sufficient condition for the existence of a spacelike solution, with prescribed mean curvature, which is the graph of a function defined on a domain equal to the complement in $\mathbb R^n$ of the union of a finite number of bounded Lipschitz domains. The mean curvature $H=H(x,t)$ is assumed to have absolute value controlled from above by a locally bounded, $L^p$-function, $p\in [1,2n/(n+2)]$, $n\geq 3$. Comment: AMSLaTeX, 15 pages; v4: reference [37] updated |
| Databáze: | OpenAIRE |
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