The prescribed mean curvature equation for nonparametric surfaces

DOI10.1016/S0362-546X(02)00105-0zbMath1029.53070OpenAlexW2015962933MaRDI QIDQ1863488

Pablo Amster, Maria Christina Mariani

Publication date: 11 March 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(02)00105-0

zbMATH Keywords

Sobolev spaceprescribed mean curvature equationnonparametric surface

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (15)

Homoclinic solutions for a class of prescribed mean curvature Liénard equations ⋮ Optimal control of a degenerate PDE for surface shape ⋮ On the classification and evolution of bifurcation curves for a one-dimensional prescribed curvature problem with nonlinearity \(\exp(\frac{a u}{a + u})\) ⋮ Prescribed mean curvature equations under the transformation with non-orthogonal curvilinear coordinates ⋮ Homoclinic solutions for a kind of prescribed mean curvature Duffing-type equation ⋮ Mountain pass solutions to equations of \(p\)-Laplacian type. ⋮ An iteration method for solving elliptic equations ⋮ Boundary value problems for highly nonlinear inclusions governed by non-surjective \(\Phi \)-Laplacians ⋮ Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity ⋮ Exact number of solutions of a prescribed mean curvature equation ⋮ Positive solutions of the prescribed mean curvature equation with exponential critical growth ⋮ One-dimensional prescribed mean curvature equation with exponential nonlinearity ⋮ Nontrivial homoclinic solutions for prescribed mean curvature Rayleigh equations ⋮ Exact multiplicity and bifurcation diagrams of positive solutions of a one-dimensional multiparameter prescribed mean curvature problem ⋮ Periodic solutions for a prescribed mean curvature equation with multiple delays

Cites Work

• Solutions to the mean curvature equation by fixed point methods
• A Dirichlet problem for an \(H\)-system with variable \(H\)
• Existence and uniqueness of \(H\)-system's solutions with Dirichlet conditions
• The Dirichlet problem for the equation of prescribed mean curvature
• Multiple solutions ofH-systems and Rellich's conjecture
• On the plateau problem for surfaces of constant mean curvature
• The prescribed mean curvature equation with Dirichlet conditions
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