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

DOI:
https://doi.org/10.1090/S0002-9939-01-06312-2

Published electronically:
December 20, 2001

MathSciNet review:
1879955

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the Hölder estimates of weak solutions of the Cauchy problem for the general degenerate parabolic equations

with the initial data , where the diffusion function 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 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

DOI:
https://doi.org/10.1090/S0002-9939-01-06312-2

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