ABP and global Hölder estimates for fully nonlinear elliptic equations in unbounded domains

DOI10.1142/S0219199715500753zbMath1344.35036arXiv1407.7116OpenAlexW2238219805MaRDI QIDQ2809272

Isabeau Birindelli, Antonio Vitolo, Italo Capuzzo-Dolcetta

Publication date: 27 May 2016

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.7116

zbMATH Keywords

maximum principlesunbounded domainsHölder continuitynonlinear elliptic equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Viscosity solutions to PDEs (35D40)

Related Items (16)

On the strong maximum principle ⋮ Maximum principle in some unbounded domains for an elliptic operator with unbounded drift ⋮ Singular elliptic equations with directional diffusion ⋮ Existence and uniqueness of nontrivial radial solutions for \(k\)-Hessian equations ⋮ Aleksandrov-Bakelman-Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE ⋮ The Alexandroff-Bakelman-Pucci estimate via positive drift ⋮ Infinity-Laplacian type equations and their associated Dirichlet problems ⋮ Maximum Principles and Aleksandrov--Bakelman--Pucci Type Estimates for NonLocal Schrödinger Equations with Exterior Conditions ⋮ Existence of positive entire solutions of fully nonlinear elliptic equations ⋮ Maximum principle for Pucci equations with sublinear growth in \(D u\) and its applications ⋮ Comparison principles for infinity-Laplace equations in Finsler metrics ⋮ Harnack inequality and an asymptotic mean-value property for the Finsler infinity-Laplacian ⋮ Regularity properties for a class of non-uniformly elliptic Isaacs operators ⋮ Directional ellipticity on special domains: weak maximum and Phragmén-Lindelöf principles ⋮ Aleksandrov-Bakelman-Pucci maximum principle for \(L^p\)-viscosity solutions of equations with unbounded terms ⋮ Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues

Cites Work

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• On the maximum principle for second-order elliptic operators in unbounded domains
• On the Phragmén-Lindelöf principle for second-order elliptic equations
• A beginner's guide to the theory of viscosity solutions
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• User’s guide to viscosity solutions of second order partial differential equations
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Remarks on regularity of viscosity solutions for fully nonlinear uniformly elliptic PDEs with measurable ingredients.

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