On the exterior Dirichlet problem for Hessian quotient equations

DOI10.1016/j.jde.2018.01.047zbMath1392.35105arXiv1709.04712OpenAlexW2962719718MaRDI QIDQ1706619

Zhisu Li, Dongsheng Li

Publication date: 22 March 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.04712

zbMATH Keywords

Dirichlet problemPerron methodHessian quotient equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Second-order elliptic equations (35J15) Monge-Ampère equations (35J96)

Related Items

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, The exterior Dirichlet problem for the homogeneous complex \(k\)-Hessian equation, Symmetry of solutions of minimal gradient graph equations on punctured space, Asymptotic behavior of solutions of fully nonlinear equations over exterior domains, On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations, The asymptotic behavior of viscosity solutions of Monge-Ampère equations in half space, On the exterior Dirichlet problem for special Lagrangian equations

Cites Work

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• The exterior Dirichlet problem for Hessian quotient equations
• 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
• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• 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
• A Bernstein problem for special Lagrangian equations
• The space of parabolic affine spheres with fixed compact boundary
• The Bernstein problem for affine maximal hypersurfaces
• The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian
• On the improper convex affine hyperspheres
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• The Dirichlet problem for the prescribed curvature equations
• Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
• On the exterior Dirichlet problem for Hessian equations
• ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS
• A priori estimate for convex solutions to special Lagrangian equations and its application
• SOLUTION OF THE DIRICHLET PROBLEM FOR SOME EQUATIONS OF MONGE-AMPÈRE TYPE
• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• User’s guide to viscosity solutions of second order partial differential equations
• An extension to a theorem of Jörgens, Calabi, and Pogorelov
• Liouville property and regularity of a Hessian quotient equation
• Necessary and sufficient conditions on existence and convexity of solutions for Dirichlet problems of Hessian equations on exterior domains
• On the exterior Dirichlet problem for special Lagrangian equations
• Some aspects of the global geometry of entire space-like submanifolds