The generalized Dirichlet problem for equations of Monge-Ampère type

DOI10.1016/S0294-1449(16)30386-9zbMath0602.35038MaRDI QIDQ1081747

John I. E. Urbas

Publication date: 1986

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1986__3_3_209_0

zbMATH Keywords

Dirichlet problemexistenceuniquenessconvex solutionequations of Monge-Ampère type

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear boundary value problems for linear elliptic equations (35J65)

Related Items

Regularity of almost extremal solutions of Monge–Ampère equations, Fast $L^2$ Optimal Mass Transport via Reduced Basis Methods for the Monge--Ampère Equation, Global Hölder estimates for equations of Monge-Ampère type, Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation, Convergent approximation of non-continuous surfaces of prescribed Gaussian curvature, Global bifurcation and convex solutions for the Monge-Ampère equation, Boundary regularity for solutions of the equation of prescribed Gauss curvature, Regularity of generalized solutions of Monge-Ampère equations

Cites Work

• Über die Differentialgleichung \(rt-s^ 2=f\) und das Weylsche Einbettungsproblem
• The equation of prescribed Gauss curvature without boundary conditions
• Boundary regularity for solutions of the equation of prescribed Gauss curvature
• The Dirichlet problem for the multidimensional Monge-Ampère equation
• The regularity of convex regions with a metric that is regular in the Hölder classes
• On the Dirichlet problem for surfaces of prescribed mean curvature
• Sur les équations de Monge-Ampère. I
• The Dirichlet problem for the equation of prescribed Gauss curvature
• On second derivative estimates for equations of Monge-Ampère type
• Fully Nonlinear, Uniformly Elliptic Equations Under Natural Structure Conditions
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item