Local regularity for concave homogeneous complex degenerate elliptic equations dominating the Monge-Ampère equation

DOI10.1007/s10231-021-01129-yzbMath1486.35221OpenAlexW3173752709MaRDI QIDQ2118028

Soufian Abja, Guillaume Olive

Publication date: 22 March 2022

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-021-01129-y

zbMATH Keywords

Monge-Ampère equationdegenerate elliptic equationslocal regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) Complex Monge-Ampère operators (32W20)

Related Items

Determinant majorization and the work of Guo-Phong-Tong and Abja-Olive, Complex geometry and dynamical systems. Abstracts from the workshop held September 4--10, 2022, Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation, Interior estimates for p-plurisubharmonic functions

Cites Work

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• \(C^{2,\alpha}\) estimates for nonlinear elliptic equations in complex and almost complex geometry
• A local regularity of the complex Monge-Ampère equation
• Dirichlet duality and the nonlinear Dirichlet problem on Riemannian manifolds
• On the Dirichlet problem for a class of singular complex Monge-Ampère equations
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations
• The Dirichlet problem for a complex Monge-Ampère equation
• Further developments of the pluripotential theory (survey)
• On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
• On the \(C^{2,\alpha}\)-regularity of the complex Monge-Ampère equation
• A priori estimates for complex Hessian equations
• The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold
• A Remark on Bony Maximum Principle
• Dirichlet duality and the nonlinear Dirichlet problem
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• p-convexity, p-plurisubharmonicity, and the Levi problem
• Inequalities: theory of majorization and its applications