Smooth local solutions to degenerate hyperbolic Monge-Ampère equations

DOI10.1007/s40818-018-0055-yzbMath1423.35254OpenAlexW2907643113WikidataQ125369458 ScholiaQ125369458MaRDI QIDQ2273638

Tiancong Chen

Publication date: 24 September 2019

Published in: Annals of PDE (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40818-018-0055-y

zbMATH Keywords

Nash-Moser iterationexistence of local solutionsprescribed curvature problems

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Degenerate hyperbolic equations (35L80)

Related Items

Global well-posedness to the Cauchy problem of 2D inhomogeneous incompressible magnetic Bénard equations with large initial data and vacuum ⋮ Numerical methods for the hyperbolic Monge-Ampère equation based on the method of characteristics ⋮ On the prescribed negative Gauss curvature problem for graphs

Cites Work

• Unnamed Item
• Unnamed Item
• On the local isometric embedding in \(\mathbb R^3\) of surfaces with Gaussian curvature of mixed sign
• Local solutions to a class of Monge-Ampère equations of mixed type
• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• The local isometric embedding in \(R^ 3\) of 2-dimensional Riemannian manifolds with nonnegative curvature
• Existence of \(C^{\infty}\) local solutions for the Monge-Ampère equation
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• The existence of hypersurfaces of constant Gauss curvature with prescribed boundary.
• Local isometric embedding of surfaces with nonpositive Gaussian curvature.
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The local isometric embedding inR3 of two-dimensional riemannian manifolds with gaussian curvature changing sign cleanly
• Seminar on Differential Geometry. (AM-102)
• On the isometric embedding of surfaces with Gauss curvature changing sign cleanly
• Local Smooth Isometric Embeddings of Low Dimensional Riemannian Manifolds into Euclidean Spaces
• Counterexamples to the Local Solvability of Monge-Ampère Equations in the Plane
• On the Cauchy problem of degenerate hyperbolic equations
• Degenerate elliptic‐parabolic equations of second order
• Symmetric hyperbolic linear differential equations
• Local isometric embedding of two dimensional Riemannian manifolds into \(R^ 3\) with nonpositive Gaussian curvature