Abstract
AbstractWe establish Hölder continuity for locally bounded weak solutions to certain parabolic systems of porous medium type, i.e. $$\begin{aligned} \partial _t \mathbf{u}-\mathrm{div}(m|\mathbf{u}|^{m-1}D\mathbf{u})=0,\quad m>0. \end{aligned}$$
∂
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As a consequence of our local Hölder estimates, a Liouville type result for bounded global solutions is also established. In addition, sufficient conditions are given to ensure local boundedness of local weak solutions.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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