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...
Guardado en:
| Publicado: |
2019
|
|---|---|
| Materias: | |
| 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: |
| Sumario: | 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. |
|---|