Critical points of solutions of degenerate elliptic equations in the plane

DOI10.1007/s00526-009-0304-8zbMath1197.35120arXiv0812.4244OpenAlexW2014466035MaRDI QIDQ5961987

Simone Cecchini, Rolando Magnanini

Publication date: 16 September 2010

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.4244

zbMATH Keywords

critical pointsdegenerate elliptic equationsstream functionsviscosity approximations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Variational methods for second-order elliptic equations (35J20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Viscosity solutions to PDEs (35D40)

Related Items

Critical points of solutions to a kind of linear elliptic equations in multiply connected domains ⋮ Critical points of solutions to a quasilinear elliptic equation with nonhomogeneous Dirichlet boundary conditions ⋮ Explicit complex-valued solutions of the 2D eikonal equation ⋮ Symmetry of minimizers with a level surface parallel to the boundary ⋮ Critical points of solutions of sub-elliptic equations on the Heisenberg group ⋮ Hot spots in convex domains are in the tips (up to an inradius) ⋮ Critical points and level sets of Grushin-harmonic functions in the plane ⋮ Uniqueness of critical points of solutions to the mean curvature equation with Neumann and Robin boundary conditions ⋮ A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals ⋮ Critical points and geometric properties of Green's functions on open surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minimizers of convex functionals arising in random surfaces
• On p-harmonic functions in the plane and their stream functions
• On certain p-harmonic functions in the plane
• A minimum principle for the problem of torsional creep
• Critical sets of solutions to elliptic equations.
• Elliptic partial differential equations of second order
• A beginner's guide to the theory of viscosity solutions
• Hodge decomposition. A method for solving boundary value problems
• On the partial differential equation \(u_ x^ 2 u_{xx} +2u_ x u_ y u_{xy} +u_ y^ 2 u_{yy} = 0\)
• On Fully Nonlinear PDEs Derived from Variational Problems ofL^pNorms
• On a familiy of torsional creep problems.
• Some remarks concerning quasiconvexity and strong convergence
• User’s guide to viscosity solutions of second order partial differential equations
• Some Applications of the Maximum Principle in the Problem of Torsional Creep
• Elliptic Equations in Divergence Form, Geometric Critical Points of Solutions, and Stekloff Eigenfunctions
• On Complex-Valued Solutions to a Two-Dimensional Eikonal Equation. II. Existence Theorems
• On complex-valued solutions to a 2D Eikonal equation. Part three: analysis of a Bäcklund transformation
• Verallgemeinerte und exakte Lösungen des Problems der elastisch‐plastischen Torsion von Stäben

This page was built for publication: Critical points of solutions of degenerate elliptic equations in the plane