\(C^{1,1}\) solution of the Dirichlet problem for degenerate \(k\)-Hessian equations

DOI10.1016/j.na.2014.03.016zbMath1316.35103arXiv1309.4204OpenAlexW1630592470MaRDI QIDQ2447087

Chao-Jiang Xu, Qi Wang

Publication date: 24 April 2014

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

Full work available at URL: https://arxiv.org/abs/1309.4204

zbMATH Keywords

Dirichlet problemdegenerate \(k\)-Hessian equations\(C^{1,1}\)-solution

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) A priori estimates in context of PDEs (35B45) Second-order elliptic equations (35J15)

Related Items (15)

Bounded solutions of a \(k\)-Hessian equation in a ball ⋮ The Neumann problem for degenerate Hessian quotient equations ⋮ Local solvability of the \(k\)-Hessian equations ⋮ The existence and multiplicity of \(k\)-convex solutions for a coupled \(k\)-Hessian system ⋮ Boundary regularity for \(k\)-Hessian equations ⋮ Second order estimates for convex solutions of degenerate \(k\)-Hessian equations ⋮ \(C^\infty\) local solutions of elliptical \(2\)-Hessian equation in \(\mathbb{R}^3\) ⋮ Boundary blow-up solutions to the \(k\)-Hessian equation with a weakly superlinear nonlinearity ⋮ Bounded solutions of a \(k\)-Hessian equation involving a weighted nonlinear source ⋮ On a \(k\)-Hessian equation with a weakly superlinear nonlinearity and singular weights ⋮ Multiplicity of bounded solutions to the \(k\)-Hessian equation with a Matukuma-type source ⋮ A Dirichlet's principle for the \(k\)-Hessian ⋮ Boundary behavior of \(k\)-convex solutions for singular \(k\)-Hessian equations ⋮ Regularity of degenerate Hessian equations ⋮ Regularity of degenerate \(k\)-Hessian equations on closed Hermitian manifolds

Cites Work

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• The Dirichlet Problem for Degenerate Hessian Equations
• The k-Hessian Equation
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• Weak solutions of hessian equations
• On the General Notion of Fully Nonlinear Second-Order Elliptic Equations
• REGULARITY FOR MONGE-AMPERE EQUATION NEAR THE BOUNDARY

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