A priori interior gradient bounds for solutions to elliptic Weingarten equations

DOI10.1016/S0294-1449(16)30357-2zbMath0644.35041MaRDI QIDQ1102447

Nicholas J. Korevaar

Publication date: 1987

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1987__4_5_405_0

zbMATH Keywords

maximum principlesmooth solutionsprescribed mean curvature equationa priori interior gradient boundsinterior barrier surfaceWeingarten equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45)

Related Items (20)

An interior gradient estimate for the mean curvature equation of Killing graphs and applications ⋮ The Dirichlet problem for the prescribed curvature equations ⋮ Principal eigenvalues for \(k\)-Hessian operators by maximum principle methods ⋮ The interior gradient estimate for some nonlinear curvature equations ⋮ The global curvature estimate for the \(n - 2\) Hessian equation ⋮ A potential theory for the \(k\)-curvature equation ⋮ Interior Gradient Estimates for General Prescribed Curvature Equations ⋮ A priori bounds and necessary conditions for solvability of prescribed curvature equations ⋮ Isolated singularities for some types of curvature equations. ⋮ Unnamed Item ⋮ The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds ⋮ Comparison results for Hessian equations via symmetrization ⋮ The interior gradient estimate of prescribed Hessian quotient curvature equations ⋮ Unnamed Item ⋮ Interior curvature bounds for a class of curvature equations ⋮ Solution to the boundary blowup problem for \(k\)-curvature equation ⋮ Second-order estimates and regularity for fully nonlinear elliptic equations on Riemannian manifolds ⋮ The interior gradient estimate of prescribed Hessian quotient curvature equation in the hyperbolic space ⋮ Curvature estimates for convex solutions of some fully nonlinear Hessian-type equations ⋮ Singular sets for curvature equation of order \(k\)

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