Classical solutions of singular Monge-Ampère equations in a ball

DOI10.1016/J.JMAA.2004.11.019zbMath1141.35373OpenAlexW1966242161MaRDI QIDQ1771397

Carlos Alberto Santos, José Valdo A. Goncalves

Publication date: 21 April 2005

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.2004.11.019

zbMATH Keywords

Fixed pointsExistence of solutionsShooting methodRadially symmetric solutionsSingular Monge-Ampère equations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60)

Related Items (12)

Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior ⋮ On the solutions to weakly coupled system of \(\boldsymbol{k_i}\)-Hessian equations ⋮ Radially symmetric convex solutions for Dirichlet problems of Monge-Ampère equations ⋮ A type of Brézis-Oswald problem to the \(\Phi\)-Laplacian operator with very singular term ⋮ Multiple sign-changing radially symmetric solutions in a general class of quasilinear elliptic equations ⋮ Triple nontrivial radial convex solutions of systems of Monge-Ampère equations ⋮ Refined second boundary behavior of the unique strictly convex solution to a singular Monge-Ampère equation ⋮ Refined boundary behavior of the unique convex solution to a singular Dirichlet problem for the Monge-Ampère equation ⋮ On radial solutions for Monge–Ampère equations ⋮ Positive solutions of two-point boundary value problems for Monge-Ampère equations ⋮ Singular boundary value problems for the Monge-Ampère equation ⋮ About positive \(W_{\mathrm{loc}}^{1,\Phi}(\Omega)\)-solutions to quasilinear elliptic problems with singular semilinear term

Cites Work

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• Existence and uniqueness of positive solutions to a semilinear elliptic problem in \(\mathbb{R}^N\)
• On singular boundary value problems for the Monge-Ampère operator
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)

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