On the Dirichlet problem for Monge-Ampère type equations

DOI10.1007/s00526-013-0619-3zbMath1292.35131arXiv1303.0595OpenAlexW2067052283WikidataQ59258813 ScholiaQ59258813MaRDI QIDQ2445466

Feida Jiang, Neil S. Trudinger, Xiao-Ping Yang

Publication date: 14 April 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0595

zbMATH Keywords

Dirichlet problemMonge-Ampère equationsubsolutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Transportation, logistics and supply chain management (90B06) Nonlinear elliptic equations (35J60)

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Cites Work

• Unnamed Item
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• On the regularity of solutions of optimal transportation problems
• Boundary regularity of maps with convex potentials. II
• On strict convexity and continuous differentiability of potential functions in optimal transportation
• On Monge-Ampère type equations arising in optimal transportation problems
• On Pogorelov estimates for Monge-Ampère type equations
• Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
• Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions
• Boundary-value problems on \(S^ n\) for surfaces of constant Gauss curvature
• On the Dirichlet problem for Hessian equations
• Elliptic partial differential equations of second order
• A priori estimate of \(\| u\|(C^ 2(\Omega^-)\)-norm) for convex solutions of the Dirichlet problem for the Monge-Ampère equations
• Regularity of potential functions of the optimal transportation problem
• The Dirichlet problem for the prescribed curvature equations
• Some existence results for fully nonlinear elliptic equations of monge-ampère type
• On the second boundary value problem for Monge-Ampère type equations and optimal transportation
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Correction to: The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampere equation
• The Regularity of Mappings with a Convex Potential
• On the second boundary value problem for equations of Monge-Ampère type.
• On the existence and regularity of hypersurfaces of prescribed Gauss curvature with boundary
• On the design of a reflector antenna
• Conformal metrics with prescribed curvature functions on manifolds with boundary