Regularity of Viscous Solutions for a Degenerate Non-linear Cauchy Problem

Authors

Eric Hern\u00e1ndez Sastoque Departamento de Matem\u00e1ticas, Universidad de Magdalena, Santa Marta, Colombia
Christian Klingenberg Department of Mathematics, Wurzburg University, Germany
Leonardo Rend\u00f3n Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, Bogot\u00e1
Juan C. Juajibioy Departamento de Ciencias Naturales Y Ex\u00e1ctas, Fundaci\u00f3n Universidad Autonoma de Colombia, Bogot\u00e1

DOI:

https://doi.org/10.4208/jpde.v29.n1.2

Keywords:

Viscosity solution;Hölder estimates;Hölder continuity

Abstract

" We consider the Cauchy problem for a class of nonlinear degenerate parabolic equation with forcing. By using the vanishing viscosity method it is possible to construct a generalized solution. Moreover, this solution is a Lipschitz function on the spatial variable and H\u00f6lder continuous with exponent 1\/2 on the temporal variable."

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Published

2016-03-05

Issue

Vol. 29 No. 1 (2016)

Section

Articles