Convexity of solutions and \(C^{1,1}\) estimates for fully nonlinear elliptic equations

DOI10.1016/j.matpur.2006.01.003zbMath1206.35108OpenAlexW2090206169MaRDI QIDQ995460

Cyril Imbert

Publication date: 3 September 2007

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2006.01.003

zbMATH Keywords

\(C^{11}\) estimateAlexandroff estimateconvexity and partial convexity of viscosity solutionssubset of convex envelope of epi-pointed functions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (9)

Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations ⋮ Representation, relaxation and convexity for variational problems in Wiener spaces ⋮ Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations ⋮ Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions ⋮ Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations ⋮ Semiconvexity of Viscosity Solutions to Fully Nonlinear Evolution Equations via Discrete Games ⋮ Inhomogeneous Hopf-Oleĭnik lemma and regularity of semiconvex supersolutions via new barriers for the Pucci extremal operators ⋮ An obstacle problem arising in large exponent limit of power mean curvature flow equation ⋮ Optimal control of diffusion processes with terminal constraint in law

Cites Work

• Interior a priori estimates for solutions of fully nonlinear equations
• Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations
• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• Quadratic growth of solutions of fully nonlinear second order equations in \({\mathbb{R}{}}^ n\)
• Convex viscosity solutions and state constraints
• Optimal Control with State-Space Constraint I
• User’s guide to viscosity solutions of second order partial differential equations
• What is the Subdifferential of the Closed Convex Hull of a Function?
• On viscosity solutions of fully nonlinear equations with measurable ingredients
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