Hölder estimates of solutions to a degenerate diffusion equation
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- by Yunguang Lu PDF
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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{equation*} u_{t}= \Delta G(u)+ \sum \limits _{j=1}^{N}f_{j}(u)_{x_{j}}+h(u), \end{equation*} 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.References
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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
- Received by editor(s): April 12, 2000
- Published electronically: December 20, 2001
- Communicated by: Suncica Canic
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1879955