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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Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09262601_v50_n2_p149_daSilva |
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todo:paper_09262601_v50_n2_p149_daSilva2023-10-03T15:46:34Z Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications da Silva, J.V. Dos Prazeres, D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 da Silva, J.V. Dos Prazeres, D. 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. |
format |
JOUR |
author |
da Silva, J.V. Dos Prazeres, D. |
author_facet |
da Silva, J.V. Dos Prazeres, D. |
author_sort |
da Silva, J.V. |
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 |
url |
http://hdl.handle.net/20.500.12110/paper_09262601_v50_n2_p149_daSilva |
work_keys_str_mv |
AT dasilvajv schaudertypeestimatesforflatviscositysolutionstononconvexfullynonlinearparabolicequationsandapplications AT dosprazeresd schaudertypeestimatesforflatviscositysolutionstononconvexfullynonlinearparabolicequationsandapplications |
_version_ |
1782027818132045824 |