A priori bounds and necessary conditions for solvability of prescribed curvature equations

DOI10.1007/BF02568424zbMath0703.35070MaRDI QIDQ915980

Neil S. Trudinger

Publication date: 1990

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155491

zbMATH Keywords

Dirichlet problemexistencehigher order mean curvature equationsPoincaré and Sobolev type inequalities

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) A priori estimates in context of PDEs (35B45)

Related Items

The Dirichlet problem for degenerate curvature equations, The Dirichlet problem for the prescribed curvature equations, Isoperimetric inequalities for quermassintegrals, The dirichlet problem for a class of fully nonlinear elliptic equations, On a class of equations of Monge-Ampère type, Estimate of the gradient of a solution of the Dirichlet problem for Monge-Ampère type equations in a domain with nonsmooth boundary, An extremal case of the equation of prescribed Weingarten curvature, A potential theory for the \(k\)-curvature equation, \(\mathbb R\)-mapping based method for designing of form cutting tool for sculptured surface machining., Unnamed Item, Interior curvature bounds for a class of curvature equations, On the Aleksandrov-Bakel'man-Pucci estimate for some elliptic and parabolic nonlinear operators, Admissible solutions to Hessian equations with exponential growth, Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature, Surfaces with prescribed curvature. I

Cites Work

• A priori interior gradient bounds for solutions to elliptic Weingarten equations
• Una maggiovazione integrale per le curvature delle ipersuperfici minimali
• The Dirichlet problem for the prescribed curvature equations
• The Dirichlet problem for the equation of prescribed Gauss curvature
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item