Maximum principle for fully nonlinear equations via the iterated comparison function method

DOI10.1007/s00208-007-0125-zzbMath1387.35243OpenAlexW2056968120MaRDI QIDQ2458845

Shigeaki Koike, Andrzej Świȩch

Publication date: 5 November 2007

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-007-0125-z

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (25)

Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients ⋮ Solvability of uniformly elliptic fully nonlinear PDE ⋮ Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients ⋮ Aleksandrov-Bakelman-Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE ⋮ Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations ⋮ Principal spectral curves for Lane-Emden fully nonlinear type systems and applications ⋮ Calderón-Zygmund estimates for the fully nonlinear obstacle problem with super-linear Hamiltonian terms and unbounded ingredients ⋮ \(C^{1,\alpha}\)-regularity for solutions of degenerate/singular fully nonlinear parabolic equations ⋮ Krylov's Boundary Gradient Type Estimates for Solutions to Fully Nonlinear Differential Inequalities with Quadratic Growth on the Gradient ⋮ A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient ⋮ LYAPUNOV-TYPE INEQUALITY FOR EXTREMAL PUCCI’S EQUATIONS ⋮ On the growth of positive entire solutions of elliptic PDEs and their gradients ⋮ Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains ⋮ Maximum principle for Pucci equations with sublinear growth in \(D u\) and its applications ⋮ Singular solutions of fully nonlinear elliptic equations and applications ⋮ The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients ⋮ On unique continuation principles for some elliptic systems ⋮ Regularity estimates for fully nonlinear elliptic PDEs with general Hamiltonian terms and unbounded ingredients ⋮ Regularity properties for a class of non-uniformly elliptic Isaacs operators ⋮ Pointwise properties of \(L^p\)-viscosity solutions of uniformly elliptic equations with quadratically growing gradient terms ⋮ Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications ⋮ Transport equations with nonlocal diffusion and applications to Hamilton-Jacobi equations ⋮ \(C^{1,\alpha}\) regularity for fully nonlinear elliptic equations with superlinear growth in the gradient ⋮ \({\mathcal{C}}^{1, \gamma }\) regularity for singular or degenerate fully nonlinear equations and applications ⋮ Aleksandrov-Bakelman-Pucci maximum principle for \(L^p\)-viscosity solutions of equations with unbounded terms

Cites Work

• Interior a priori estimates for solutions of fully nonlinear equations
• The \(L^ p\)-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations
• Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation
• \(W^{1,p}\)-interior estimates for solutions of fully nonlinear, uniformly elliptic equations
• Maximum principle and existence of \(L^p\)-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms
• On an Aleksandrov-Bakel'Man Type Maximum Principle for Second-Order Parabolic Equations
• On the regularity theory of fully nonlinear parabolic equations: I
• A nonlinear fabes—stroock result
• Remarks on nonlinear uniformly parabolic equations
• L^p- Theory for fully nonlinear uniformly parabolic equations
• On the alexandroff‐bakelman‐pucci estimate and the reversed hölder inequality for solutions of elliptic and parabolic equations
• On viscosity solutions of fully nonlinear equations with measurable ingredients
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