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Abstract:

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.

Registro:

Documento: Artículo
Título:Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
Autor:da Silva, J.V.; Dos Prazeres, D.
Filiación:Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria - Pabellón I (1428) Av. Cantilo s/n, Buenos Aires, Argentina
Palabras clave:Flat viscosity solutions; Fully nonlinear parabolic equations; Schauder type estimates
Año:2019
Volumen:50
Número:2
Página de inicio:149
Página de fin:170
DOI: http://dx.doi.org/10.1007/s11118-017-9677-z
Título revista:Potential Analysis
Título revista abreviado:Potential Anal.
ISSN:09262601
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_09262601_v50_n2_p149_daSilva

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Citas:

---------- APA ----------
da Silva, J.V. & Dos Prazeres, D. (2019) . Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications. Potential Analysis, 50(2), 149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z
---------- CHICAGO ----------
da Silva, J.V., Dos Prazeres, D. "Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications" . Potential Analysis 50, no. 2 (2019) : 149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z
---------- MLA ----------
da Silva, J.V., Dos Prazeres, D. "Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications" . Potential Analysis, vol. 50, no. 2, 2019, pp. 149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z
---------- VANCOUVER ----------
da Silva, J.V., Dos Prazeres, D. Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications. Potential Anal. 2019;50(2):149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z