Maximal hypersurfaces over exterior domains

Guo, Hong; Yuan, Yu

doi:10.48550/arxiv.1903.00787

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Introduction and Statement Of The Results1

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2020

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“…In particular, it holds for H = 0 and, in such a case, gives the existence of a maximal hypersurface on the exterior domain Ω c . Previous existence (and uniqueness, with respect to a given asymptotic profile) results for the Dirichlet problem of maximal graphs on an exterior domain of the Minkowski spacetime have been recently obtained in [30]. Existence and multiplicity results for radial solutions outside a ball, with homogeneous boundary condition, have been obtained in [42] for a separable-variables H which is also radial in the x variable.…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Spacelike graphs with prescribed mean curvature on exterior domains in the Minkowski spacetime

Bartolo,

Caponio,

Pomponio

2020

Preprint

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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 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 ∈ [1, 2n/(n + 2)], n ≥ 3.

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Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%