On a class of generalized Monge–Ampère type equations

DOI10.1142/S0219199719500056zbMath1450.35262OpenAlexW2913188421MaRDI QIDQ3299005

Lan Tang, Weifeng Qiu

Publication date: 17 July 2020

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199719500056

zbMATH Keywords

convex functiongeneralized solutionMonge-Ampère equationconvex domainsub-differential

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Monge-Ampère equations (35J96)

Cites Work

• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• A priori estimate of \(\| u\|(C^ 2(\Omega^-)\)-norm) for convex solutions of the Dirichlet problem for the Monge-Ampère equations
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• The Monge–Ampère equation and its link to optimal transportation
• BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Weakly Differentiable Functions
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• On the regularity of the solution of then-dimensional Minkowski problem
• REGULARITY FOR MONGE-AMPERE EQUATION NEAR THE BOUNDARY
• Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation
• The Monge-Ampère equation
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