Uniqueness of critical points and maximum principles of the singular minimal surface equation

DOI10.1016/j.jde.2018.09.024zbMath1406.35008OpenAlexW2892706846MaRDI QIDQ1710726

Rafael López

Publication date: 23 January 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.09.024

zbMATH Keywords

Dirichlet problemnodal linebounded strictly convex domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Quasilinear elliptic equations with mean curvature operator (35J93) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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What Is the Shape of a Cupola? ⋮ The two-dimensional analogue of the Lorentzian catenary and the Dirichlet problem ⋮ A Weierstrass type representation for translating solitons and singular minimal surfaces ⋮ Geometric and architectural aspects of the singular minimal surface equation ⋮ Geometry of \([\varphi, {\mathbf{e}}_3\)-minimal surfaces in \(\mathbb{R}^3\)] ⋮ Ruled singular minimal surfaces ⋮ Gradient estimates for the constant mean curvature equation in hyperbolic space ⋮ A dome subjected to compression forces: a comparison study between the mathematical model, the catenary rotation surface and the paraboloid

Cites Work

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• A minimum principle for a soap film problem in \({\mathbb{R}^{2}}\)
• Critical points of solutions to quasilinear elliptic problems
• Hölder continuity for continuous solutions of the singular minimal surface equation with arbitrary zero set
• On a singular variational integral with linear growth. I: Existence and regularity of minimizers
• The \(n\)-dimensional analogue of the catenary: Existence and non-existence
• Boundary regularity for solutions of a singular variational problem with linear growth
• The two-dimensional analogue of the catenary
• Eigenfunctions and nodal sets
• A minimum principle for the problem of torsional creep
• Sharp size estimates for capillary free surfaces without gravity.
• Invariant singular minimal surfaces
• A sharp height estimate for the spacelike constant mean curvature graph in the Lorentz-Minkowski space
• On some estimates for a fluid surface in a short capillary tube
• A symmetry problem in potential theory
• The Dirichlet problem for the minimal hypersurface equation on arbitrary domains of a Riemannian manifold
• Local behavior of solutions of general linear elliptic equations
• A NONEXISTENCE THEOREM FOR THE TWO-DIMENSIONAL AMLOGUE OF THE CATENARY
• Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature
• Bernstein results for symmetric minimal surfaces of controlled growth
• Compact singular minimal surfaces with boundary
• Maximum principles for energy stationary hypersurfaces
• On nonlinear elliptic partial differential equations and hölder continuity

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