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Hölder estimates of solutions to a degenerate diffusion equation

Author: Yunguang Lu
Journal: Proc. Amer. Math. Soc. 130 (2002), 1339-1343
MSC (2000): Primary 35K55, 35K65, 35D10, 35K15
Published electronically: December 20, 2001
MathSciNet review: 1879955
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Abstract: This paper is concerned with the Hölder estimates of weak solutions of the Cauchy problem for the general degenerate parabolic equations

\begin{displaymath}u_{t}= \Delta G(u)+ \sum \limits _{j=1}^{N}f_{j}(u)_{x_{j}}+h(u), \end{displaymath}

with the initial data $u(x,0)=u_{0}(x_1,x_2,\dots,x_N)$, where the diffusion function $G(u)$ can be a constant on a nonzero measure set, such as the equations of two-phase Stefan type. Some explicit Hölder exponents of the composition function $G(u)$ with respect to the space variables are obtained by using the maximum principle.

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Additional Information

Yunguang Lu
Affiliation: Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia, Bogotá, Colombia – and – Department of Mathematics, University of Science & Technology of China, Hefei, People’s Republic of China

Keywords: Degenerate parabolic equation, H\"older solution, maximum principle
Received by editor(s): April 12, 2000
Published electronically: December 20, 2001
Communicated by: Suncica Canic
Article copyright: © Copyright 2001 American Mathematical Society

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