Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications

In this manuscript we establish Schauder type estimates for viscosity solutions with small enough oscillation to non-convex fully nonlinear second order parabolic equations of the following form ∂u∂t−F(x,t,D2u)=f(x,t)inQ1=B1×(−1,0],provided that the source f and the coefficients of F are Dini contin...

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Detalles Bibliográficos
Publicado: 2019
Materias:
Flat viscosity solutions
Fully nonlinear parabolic equations
Schauder type estimates
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09262601_v50_n2_p149_daSilva
http://hdl.handle.net/20.500.12110/paper_09262601_v50_n2_p149_daSilva
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09262601_v50_n2_p149_daSilva
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spelling paper:paper_09262601_v50_n2_p149_daSilva2023-06-08T15:51:33Z Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications Flat viscosity solutions Fully nonlinear parabolic equations Schauder type estimates In this manuscript we establish Schauder type estimates for viscosity solutions with small enough oscillation to non-convex fully nonlinear second order parabolic equations of the following form ∂u∂t−F(x,t,D2u)=f(x,t)inQ1=B1×(−1,0],provided that the source f and the coefficients of F are Dini continuous functions. Furthermore, for problems with merely continuous data, we prove that such solutions are parabolically C1,Log-Lip smooth. Finally, we put forward a number of applications consequential of our estimates, which include a partial regularity result and a theorem of Schauder type for classical solutions. © 2017, Springer Science+Business Media B.V., part of Springer Nature. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09262601_v50_n2_p149_daSilva http://hdl.handle.net/20.500.12110/paper_09262601_v50_n2_p149_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 Flat viscosity solutions
Fully nonlinear parabolic equations
Schauder type estimates
spellingShingle Flat viscosity solutions
Fully nonlinear parabolic equations
Schauder type estimates
Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
topic_facet Flat viscosity solutions
Fully nonlinear parabolic equations
Schauder type estimates
description In this manuscript we establish Schauder type estimates for viscosity solutions with small enough oscillation to non-convex fully nonlinear second order parabolic equations of the following form ∂u∂t−F(x,t,D2u)=f(x,t)inQ1=B1×(−1,0],provided that the source f and the coefficients of F are Dini continuous functions. Furthermore, for problems with merely continuous data, we prove that such solutions are parabolically C1,Log-Lip smooth. Finally, we put forward a number of applications consequential of our estimates, which include a partial regularity result and a theorem of Schauder type for classical solutions. © 2017, Springer Science+Business Media B.V., part of Springer Nature.
title Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
title_short Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
title_full Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
title_fullStr Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
title_full_unstemmed Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
title_sort schauder type estimates for “flat” viscosity solutions to non-convex fully nonlinear parabolic equations and applications
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09262601_v50_n2_p149_daSilva
http://hdl.handle.net/20.500.12110/paper_09262601_v50_n2_p149_daSilva
_version_ 1768546166942728192

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