Sharp regularity estimates for second order fully nonlinear parabolic equations

We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form (Formula Presented.)where F is elliptic with respect to the Hessian argument and f∈ Lp , q(Q1). The quantity Ξ(n,p,q):=np+2q determines to which regularity regime a solution of (Eq) belongs...

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Publicado: 2017
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35B65
35K10
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v369_n3-4_p1623_daSilva
http://hdl.handle.net/20.500.12110/paper_00255831_v369_n3-4_p1623_daSilva
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00255831_v369_n3-4_p1623_daSilva
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spelling paper:paper_00255831_v369_n3-4_p1623_daSilva2023-06-08T14:53:20Z Sharp regularity estimates for second order fully nonlinear parabolic equations 35B65 35K10 We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form (Formula Presented.)where F is elliptic with respect to the Hessian argument and f∈ Lp , q(Q1). The quantity Ξ(n,p,q):=np+2q determines to which regularity regime a solution of (Eq) belongs. We prove that when 1 < Ξ (n, p, q) < 2 - ϵF, solutions are parabolically α-Hölder continuous for a sharp, quantitative exponent 0 < α(n, p, q) < 1. Precisely at the critical borderline case, Ξ (n, p, q) = 1 , we obtain sharp parabolic Log-Lipschitz regularity estimates. When 0 < Ξ (n, p, q) < 1 , solutions are locally of class C1+σ,1+σ2 and in the limiting case Ξ (n, p, q) = 0 , we show parabolic C1 , Log-Lip regularity estimates provided F has “better” a priori estimates. © 2016, Springer-Verlag Berlin Heidelberg. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v369_n3-4_p1623_daSilva http://hdl.handle.net/20.500.12110/paper_00255831_v369_n3-4_p1623_daSilva
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 35B65
35K10
spellingShingle 35B65
35K10
Sharp regularity estimates for second order fully nonlinear parabolic equations
topic_facet 35B65
35K10
description We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form (Formula Presented.)where F is elliptic with respect to the Hessian argument and f∈ Lp , q(Q1). The quantity Ξ(n,p,q):=np+2q determines to which regularity regime a solution of (Eq) belongs. We prove that when 1 < Ξ (n, p, q) < 2 - ϵF, solutions are parabolically α-Hölder continuous for a sharp, quantitative exponent 0 < α(n, p, q) < 1. Precisely at the critical borderline case, Ξ (n, p, q) = 1 , we obtain sharp parabolic Log-Lipschitz regularity estimates. When 0 < Ξ (n, p, q) < 1 , solutions are locally of class C1+σ,1+σ2 and in the limiting case Ξ (n, p, q) = 0 , we show parabolic C1 , Log-Lip regularity estimates provided F has “better” a priori estimates. © 2016, Springer-Verlag Berlin Heidelberg.
title Sharp regularity estimates for second order fully nonlinear parabolic equations
title_short Sharp regularity estimates for second order fully nonlinear parabolic equations
title_full Sharp regularity estimates for second order fully nonlinear parabolic equations
title_fullStr Sharp regularity estimates for second order fully nonlinear parabolic equations
title_full_unstemmed Sharp regularity estimates for second order fully nonlinear parabolic equations
title_sort sharp regularity estimates for second order fully nonlinear parabolic equations
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v369_n3-4_p1623_daSilva
http://hdl.handle.net/20.500.12110/paper_00255831_v369_n3-4_p1623_daSilva
_version_ 1768543312461955072

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