Boundary regularity for \(k\)-Hessian equations

DOI10.1007/s10114-023-0066-9zbMath1530.35096OpenAlexW4389444966MaRDI QIDQ6145660

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Publication date: 9 January 2024

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-023-0066-9

zbMATH Keywords

Dirichlet problem\(k\)-Hessian equationsymmetric mean

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Affine differential geometry (53A15) Boundary value problems for second-order elliptic systems (35J57)

Cites Work

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• Local solvability of the \(k\)-Hessian equations
• Bernstein theorem and regularity for a class of Monge-Ampère equations
• The Monge-Ampère equation and its applications
• Schauder estimates for degenerate Monge-Ampère equations and smoothness of the eigenfunctions
• Singularity and decay estimates for the conformal \(k\)-hessian equation via Liouville-type theorems
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• Optimal boundary regularity for a singular Monge-Ampère equation
• Global regularity for a class of Monge-Ampère type equations
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• \(C^{1,1}\) solution of the Dirichlet problem for degenerate \(k\)-Hessian equations
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Existence and uniqueness of nontrivial radial solutions for \(k\)-Hessian equations
• The Dirichlet problem for the equation of prescribed Gauss curvature
• The Dirichlet Problem for Degenerate Hessian Equations
• The k-Hessian Equation
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• Hessian equations with infinite Dirichlet boundary
• Inequalities

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