Remark on the anisotropic prescribed mean curvature equation on arbitrary domains

DOI10.1007/S00209-009-0476-0zbMath1186.35088OpenAlexW2043333523MaRDI QIDQ848825

Thomas Marquardt

Publication date: 23 February 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-009-0476-0

zbMATH Keywords

Dirichlet problemanisotropic prescribed mean curvatureboundary gradient estimate

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) A priori estimates in context of PDEs (35B45) Quasilinear elliptic equations with mean curvature operator (35J93)

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Dirichlet problem for anisotropic prescribed mean curvature equation on unbounded domains ⋮ The Dirichlet problem on a strip for the \(\alpha\)-translating soliton equation ⋮ The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions ⋮ A prescribed anisotropic mean curvature equation modeling the corneal shape: a paradigm of nonlinear analysis ⋮ Radial solutions of the Dirichlet problem for a class of quasilinear elliptic equations arising in optometry ⋮ Existence of translating solutions to the flow by powers of mean curvature on unbounded domains ⋮ Surfaces of prescribed mean curvature vector in semi-Riemannian manifolds ⋮ The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz-Minkowski space ⋮ Minimum principles and a priori estimates for some translating soliton type problems ⋮ Prescribed mean curvature equation on torus ⋮ Rotational hypersurfaces of prescribed mean curvature ⋮ The Dirichlet problem for a prescribed mean curvature equation ⋮ Invariant hypersurfaces with linear prescribed mean curvature ⋮ The translating soliton equation ⋮ Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape

Cites Work

• Interior gradient estimates for mean curvature equations
• On the Dirichlet problem for surfaces of prescribed mean curvature
• Elliptic partial differential equations of second order
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• The Dirichlet problem for graphs of prescribed anisotropic mean curvature in ℝn+1

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