The exterior Dirichlet problem for Hessian quotient equations

DOI10.1016/J.JMAA.2012.03.034zbMath1250.35098OpenAlexW2051111458MaRDI QIDQ432413

Limei Dai, Hai Gang Li

Publication date: 4 July 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.03.034

zbMATH Keywords

viscosity solutionsexterior Dirichlet problemHessian quotient equationsreverse MacLaurin inequality

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Viscosity solutions to PDEs (35D40)

Related Items (6)

Exterior problems of parabolic Monge-Ampère equations for \(n=2\) ⋮ Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations ⋮ The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations ⋮ On the exterior Dirichlet problem for Hessian quotient equations ⋮ Existence of viscosity solutions for Hessian equations in exterior domains ⋮ On the exterior Dirichlet problem for special Lagrangian equations

Cites Work

• Unnamed Item
• The Dirichlet problem for Hessian quotient equations in exterior domains
• On uniqueness and existence of viscosity solutions to Hessian equations in exterior domains
• Partial decay on simple manifolds
• Calibrated geometries
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• An extension of a theorem by K. Jörgens and a maximum principle at infinity for parabolic affine spheres
• On the Dirichlet problem for Hessian equations
• The space of parabolic affine spheres with fixed compact boundary
• The Bernstein problem for affine maximal hypersurfaces
• The local regularity for strong solutions of the Hessian quotient equation
• On the improper convex affine hyperspheres
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
• A priori estimate for convex solutions to special Lagrangian equations and its application
• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• User’s guide to viscosity solutions of second order partial differential equations
• Weak solutions of hessian equations
• An extension to a theorem of Jörgens, Calabi, and Pogorelov
• Liouville property and regularity of a Hessian quotient equation
• Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions
• Hessian equations with infinite Dirichlet boundary

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