Necessary and sufficient conditions on existence and convexity of solutions for Dirichlet problems of Hessian equations on exterior domains

DOI10.1090/S0002-9939-2012-11738-1zbMath1266.35043MaRDI QIDQ4911831

Chong Wang, Ji Guang Bao

Publication date: 20 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

existenceasymptotic behaviorconvexityradial solutionnecessary and sufficient conditionexterior Dirichlet problemHessian equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Monge-Ampère equations (35J96)

Related Items (17)

Bounded solutions of a \(k\)-Hessian equation in a ball ⋮ The exterior Dirichlet problems of Monge-Ampère equations in dimension two ⋮ Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations ⋮ On the exterior Dirichlet problem for Hessian equations ⋮ Existence and uniqueness of nontrivial radial solutions for \(k\)-Hessian equations ⋮ The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations ⋮ Existence for translating solutions of Gauss curvature flow on exterior domains ⋮ Parabolic Hessian equations outside a bowl-shaped domain ⋮ On the exterior Dirichlet problem for Hessian quotient equations ⋮ The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian ⋮ New results of coupled system of \(k\)-Hessian equations ⋮ Bounded solutions of a \(k\)-Hessian equation involving a weighted nonlinear source ⋮ On the exterior Dirichlet problem for Monge-Ampère equations ⋮ On the exterior Dirichlet problem for the Monge-Ampère equation in dimension two ⋮ Multiplicity of bounded solutions to the \(k\)-Hessian equation with a Matukuma-type source ⋮ Existence and nonexistence to exterior Dirichlet problem for Monge-Ampère equation ⋮ Boundary behavior of \(k\)-convex solutions for singular \(k\)-Hessian equations

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