On the Existence of Smooth Solutions for Fully Nonlinear Parabolic Equations with Measurable “Coefficients” without Convexity Assumptions

DOI10.1080/03605302.2012.756013zbMath1479.35526arXiv1208.4373OpenAlexW2733610606MaRDI QIDQ2841177

Hongjie Dong, Nicolai V. Krylov

Publication date: 24 July 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.4373

zbMATH Keywords

finite differencesBellman's equationsapproximating equationterminal-boundary condition

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Discrete version of topics in analysis (39A12) Weak solutions to PDEs (35D30)

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Lorentz estimates for fully nonlinear parabolic and elliptic equations ⋮ Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations ⋮ Sturm attractors for fully nonlinear parabolic equations ⋮ Local estimates for fully nonlinear parabolic equations in weighted spaces ⋮ Weighted \(L^{p(\cdot)}\)-regularity for fully nonlinear parabolic equations ⋮ The \(W^{1,2}_{( p,q )}\)-solvability for a class of fully nonlinear parabolic equations ⋮ \( W^{2, p} \)-regularity for asymptotically regular fully nonlinear elliptic and parabolic equations with oblique boundary values

Cites Work

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• On a representation of fully nonlinear elliptic operators in terms of pure second order derivatives and its applications
• The rate of convergence of finite-difference approximations for parabolic bellman equations with Lipschitz coefficients in cylindrical domains
• Singular viscosity solutions to fully nonlinear elliptic equations
• Good and viscosity solutions of fully nonlinear elliptic equations
• On the regularity theory of fully nonlinear parabolic equations: I
• L^p- Theory for fully nonlinear uniformly parabolic equations

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