Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order

DOI10.1016/S0294-1449(16)30309-2zbMath0734.35033MaRDI QIDQ810744

Michael G. Crandall

Publication date: 1989

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1989__6_6_419_0

zbMATH Keywords

viscosity solutionsfully nonlinearsub-differentialssuperdifferentials

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Degenerate parabolic equations (35K65) Degenerate elliptic equations (35J70) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Continuity and differentiation questions (26B05)

Related Items (17)

An optimal property of \(\ell\)-minimal surfaces in viscosity interpretation ⋮ On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on nonsmooth domains ⋮ Fully nonlinear Neumann type boundary conditions for first-order Hamilton–Jacobi equations ⋮ User’s guide to viscosity solutions of second order partial differential equations ⋮ Hölder behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg group ⋮ On weak critical posets with respect to the positive definiteness of a quadratic Tits form. ⋮ Sub-hessians, super-hessians and conjugation ⋮ Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence ⋮ On serial posets with positive-definite quadratic Tits form. ⋮ A comparison principle for some types of elliptic equations ⋮ Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. V: Unbounded linear terms and \(B\)-continuous solutions ⋮ Approximate Solutions to First and Second Order Quasilinear Evolution Equations via Nonlinear Viscosity ⋮ \(G\)-Lévy processes under sublinear expectations ⋮ Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III: Uniqueness of viscosity solutions for general second-order equations ⋮ Mini review of fundamental notions in the theory of fully nonlinear elliptic second-order differential equations ⋮ Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE's ⋮ Subsolutions for abstract evolution equations.

Cites Work

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• Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations
• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• A Uniqueness Result for Viscosity Solutions of Second Order Fully Nonlinear Partial Differential Equations

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