Regularity of a class of quasilinear degenerate elliptic equations

DOI10.1006/aima.1997.1677zbMath0892.35036OpenAlexW1997032851MaRDI QIDQ1378456

Pengfei Guan

Publication date: 11 February 1998

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1997.1677

zbMATH Keywords

\(C^\infty\) regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70)

Related Items (17)

Isometric embedding with nonnegative Gauss curvature under the graph setting ⋮ Gevrey regularity of subelliptic Monge-Ampère equations in the plane ⋮ On solvability of two-dimensional \(L_{p}\)-Minkowski problem. ⋮ \(C^ 2\) a priori estimates for degenerate Monge-Ampère equations ⋮ Regularity of subelliptic Monge-Ampère equations ⋮ A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations ⋮ Boundedness and regularity of solutions of degenerate elliptic partial differential equations ⋮ A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations ⋮ Regularity of degenerate Monge-Ampère and prescribed Gaussian curvature equations in two dimensions ⋮ On Monge-Ampère equations with homogenous right-hand sides ⋮ Regularity of subelliptic Monge-Ampère equations in the plane ⋮ Interior $C^2$ estimate for Monge-Ampère equation in dimension two ⋮ Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations ⋮ The Weyl problem of isometric immersions revisited ⋮ Partial Legendre transforms of non-linear equations ⋮ On the Dirichlet problem for degenerate Monge-Ampère equations. ⋮ Regularity of the homogeneous Monge-Ampère equation

Cites Work

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• Balls and metrics defined by vector fields. I: Basic properties
• Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions
• Pseudodifferential operators and nonlinear PDE
• The Weyl problem with nonnegative Gauss curvature
• Isometric embedding of the 2-sphere with non negative curvature in \(\mathbb{R}^ 3\)
• Hypoelliptic second order differential equations
• Continuity of Solutions of Parabolic and Elliptic Equations
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• On Harnack's theorem for elliptic differential equations
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Weighted Sobolev-Poincare Inequalities and Pointwise Estimates for a Class of Degenerate Elliptic Equations
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