The Dirichlet problem for the mimimal hypersurface equation with Lipschitz continuous boundary data in a Riemannian manifold

DOI10.2140/pjm.2020.307.1zbMath1445.53045OpenAlexW3047876570WikidataQ115230556 ScholiaQ115230556MaRDI QIDQ785756

Rodrigo Soares, Giovanni da Silva Nunes, Lisandra Sauer, Ari J. Aiolfi

Publication date: 10 August 2020

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2020.307.1

zbMATH Keywords

Dirichlet problem for minimal hypersurface equationLipschitz continuous boundary data

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Elliptic equations on manifolds, general theory (58J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

• Some existence results on the exterior Dirichlet problem for the minimal hypersurface equation
• Complete minimal graphs with prescribed asymptotic boundary on rotationally symmetric Hadamard surfaces
• Lower estimates for the first eigenvalue of the Laplace operator on doubly connected domains in a Riemannian manifold
• Uniqueness of \(H\)-surfaces in \(\mathbb H^2 \times \mathbb R\), \(|H|\leq 1/2\), with boundary one or two parallel horizontal circles
• Killing graphs with prescribed mean curvature
• An asymptotic theorem for minimal surfaces and existence results for minimal graphs in \({\mathbb H^2 \times \mathbb R}\)
• On the Dirichlet problem for the prescribed mean curvature equation over general domains
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• Existence and nonexistence for the exterior Dirichlet problem for the minimal surface equation in the plane.
• On solutions to the exterior Dirichlet problem for the minimal surface with catenoidal ends
• The Dirichlet problem for the minimal hypersurface equation on arbitrary domains of a Riemannian manifold
• The Dirichlet problem for the minimal surface equation with Lipschitz continuous boundary data.
• BARRIERS AND EXISTENCE RESULTS FOR A CLASS OF EQUATIONS OF MEAN CURVATURE TYPE
• The Dirichlet problem for the minimal surface equation in higher dimensions.

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