Existence and regularity of extremal solutions for a mean-curvature equation

DOI10.1016/j.jde.2010.03.026zbMath1194.53010arXiv0904.0618OpenAlexW2964230158MaRDI QIDQ982539

Antoine Mellet, Julien Vovelle

Publication date: 7 July 2010

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

Full work available at URL: https://arxiv.org/abs/0904.0618

zbMATH Keywords

regularityextremal solutionminimal solutionmean curvature equationsemi-stable solution

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items

The periodic problem for curvature-like equations with asymmetric perturbations ⋮ A weighted quasilinear equation related to the mean curvature operator ⋮ Radial solutions for a prescribed mean curvature equation with exponential nonlinearity ⋮ Extremal solutions to fourth order discontinuous functional boundary value problems ⋮ Nonexistence of solutions for prescribed mean curvature equations on a ball ⋮ Refinements to the study of electrostatic deflections: theory and experiment

Cites Work

• Existence and regularity for the problem of a pendent liquid drop
• Regularity of radial minimizers and extremal solutions of semilinear elliptic equations
• On the partial differential equations of electrostatic MEMS devices. II: Dynamic case
• Esistenza e regolarita delle ipersuperfici di curvatura media assegnata in \(R^n\)
• Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
• On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions
• Evolutionary existence proofs for the pendant drop and \(n\)-dimensional catenary problems
• On the Dirichlet problem for surfaces of prescribed mean curvature
• Capillary surfaces in negative gravitational fields
• Positive solutions of convex nonlinear eigenvalue problems
• Blow up for \(u_ t- \Delta u=g(u)\) revisited
• Regularity of minimizers for three elliptic problems: minimal cones, harmonic maps, and semilinear equations
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature
• Quasilinear Dirichlet problems driven by positive sources
• On the Partial Differential Equations of Electrostatic MEMS Devices: Stationary Case
• On pendent drops in a capillary tube
• Sharp existence results for a class of semilinear elliptic problems
• The shape of a pendant liquid drop
• Sur une classe de problemes non lineaires avec non linearite positive, croissante, convexe.
• Regularity of the extremal solution of semilinear elliptic equations
• The study of a bifurcation problem associated to an asymptotically linear function
• Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
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