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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity of viscosity solutions of a degenerate parabolic equation


Authors: Yun-Guang Lu and Liwen Qian
Journal: Proc. Amer. Math. Soc. 130 (2002), 999-1004
MSC (2000): Primary 35K55; Secondary 35K65, 35D10
Published electronically: November 9, 2001
MathSciNet review: 1873772
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the Cauchy problem for the nonlinear degenerate parabolic equation of second order

\begin{displaymath}\left\{ \begin{array}{l} u_t=u\triangle u-\gamma\vert\nabla u... ...0)=u_{0}(x) \text{in} \hspace{0.3cm} R^{N}, \end{array}\right. \end{displaymath}

and present regularity results for the viscosity solutions.


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Additional Information

Yun-Guang Lu
Affiliation: Departamento de Matematicas y Estadistica, Universidad Nacional de Colombia, Bogota, Colombia
Email: yglu@matematicas.unal.edu.co

Liwen Qian
Affiliation: Department of Computational Science, National University of Singapore, Singapore 117543
Address at time of publication: Singapore-MIT Alliance, National University of Singapore, Singapore 119260
Email: qianlw@cz3.nus.edu.sg, smaqlw@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06313-4
PII: S 0002-9939(01)06313-4
Keywords: Degenerate parabolic equation, viscosity solution, Lipschitz continuity, maximum principle
Received by editor(s): November 1, 1998
Received by editor(s) in revised form: April 10, 2000
Published electronically: November 9, 2001
Communicated by: Suncica Canic
Article copyright: © Copyright 2001 American Mathematical Society