Necessary conditions of solvability and isoperimetric estimates for some Monge-Ampère problems in the plane

DOI10.1090/S0002-9939-2014-12222-2zbMath1307.35109OpenAlexW2059029408MaRDI QIDQ5496255

Cristian Enache

Publication date: 30 January 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2014-12222-2

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Monge-Ampère equations (35J96)

Related Items (4)

Maximum principles and overdetermined problems for Hessian equations ⋮ Maximum and minimum principles for a class of Monge-Ampère equations in the plane, with applications to surfaces of constant Gauss curvature ⋮ Minimum principles and a priori estimates for some translating soliton type problems ⋮ A note on Monge-Ampère equation in \(\mathbb{R}^2\)

Cites Work

• Unnamed Item
• A minimum principle for a soap film problem in \({\mathbb{R}^{2}}\)
• Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs
• On isoperimetric gradient bounds for Poisson problems and problems of torsional creep
• Maximum principles and their applications
• A minimum principle for the problem of torsional creep
• A sharp minimum principle for the problem of torsionally rigidity
• Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE's
• Sharp size estimates for capillary free surfaces without gravity.
• Nonlinear oblique boundary value problems for Hessian equations in two dimensions
• A minimum principle for the problem of St-Venant in \({\mathbb{R}^N, N \geq 2}\)
• On some estimates for a fluid surface in a short capillary tube
• A maximum principle for some fully nonlinear elliptic equations with applications to Weingarten hypersurfaces
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The neumann problem for equations of monge-ampère type
• A necessary condition of solvability for the capillarity boundary of Monge-Ampere equations in two dimensions
• A note on the contact angle boundary condition for Monge-Ampère equations
• A Remark on Linear Elliptic Differential Equations of Second Order

This page was built for publication: Necessary conditions of solvability and isoperimetric estimates for some Monge-Ampère problems in the plane