Hölder estimates of solutions to a degenerate diffusion equation

Lu, Yunguang

doi:10.1090/S0002-9939-01-06312-2

Hölder estimates of solutions to a degenerate diffusion equation
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Proc. Amer. Math. Soc. 130 (2002), 1339-1343 Request permission

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.

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