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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00255831_v369_n3-4_p1623_daSilva |
| Aporte de: |
| id |
todo:paper_00255831_v369_n3-4_p1623_daSilva |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00255831_v369_n3-4_p1623_daSilva2023-10-03T14:36:18Z Sharp regularity estimates for second order fully nonlinear parabolic equations da Silva, J.V. Teixeira, E.V. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 da Silva, J.V. Teixeira, E.V. 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. |
| format |
JOUR |
| author |
da Silva, J.V. Teixeira, E.V. |
| author_facet |
da Silva, J.V. Teixeira, E.V. |
| author_sort |
da Silva, J.V. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00255831_v369_n3-4_p1623_daSilva |
| work_keys_str_mv |
AT dasilvajv sharpregularityestimatesforsecondorderfullynonlinearparabolicequations AT teixeiraev sharpregularityestimatesforsecondorderfullynonlinearparabolicequations |
| _version_ |
1782029780473872384 |