Equations de Monge-Ampère réelles

DOI10.1016/0022-1236(81)90081-1zbMath0465.35001OpenAlexW1994176154MaRDI QIDQ1154598

Thierry Aubin

Publication date: 1981

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(81)90081-1

zbMATH Keywords

regularityDirichlet problemmethod of upper and lower solutionsmethod of continuitybounded convex setreal Monge-Ampere equation

Mathematics Subject Classification ID

Related Items (16)

Comparison principles for weak solutions of monge–ampere equations ⋮ Global bifurcation and convex solutions for the Monge-Ampère equation ⋮ On the solvability of some monge-ampère equations ⋮ Uniqueness of least energy solutions for Monge-Ampère functional ⋮ Existence of multiple solutions to the equations of Monge-Ampère type ⋮ The Dirichlet problem for the equation of prescribed Gauss curvature ⋮ On the multiplicity of solutions to Marguerre--von Kármán membrane equations ⋮ An extension to a theorem of Jörgens, Calabi, and Pogorelov ⋮ Singular boundary value problems for the Monge-Ampère equation ⋮ Poincaré- and Sobolev- type inequalities for complex \(m\)-Hessian equations ⋮ A priori estimates and a Liouville theorem for elliptic Monge-Ampère equations ⋮ Sur les équations de Monge-Ampère. I ⋮ Multiplicity of solutions to the Marguerre-von Kármán membrane shell equations ⋮ Radially symmetric boundary value problems for real and complex elliptic Monge-Ampère equations ⋮ A priori estimates for solutions of Monge-Ampère equations ⋮ Sur les équations de Monge-Ampère. (About the Monge-Ampère equations)

Cites Work

• The Dirichlet problem for the multidimensional Monge-Ampère equation
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
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