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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weak solutions of the porous medium equation in a cylinder


Authors: Björn E. J. Dahlberg and Carlos E. Kenig
Journal: Trans. Amer. Math. Soc. 336 (1993), 701-709
MSC: Primary 35D05; Secondary 35K55, 76S05
DOI: https://doi.org/10.1090/S0002-9947-1993-1085940-6
MathSciNet review: 1085940
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Abstract: We show that if $ D \subset {{\mathbf{R}}^n}$ is a bounded domain with smooth boundary, and $ u \in {L^m}(D \times (\varepsilon ,T))$, $ u \geq 0$, solves $ \frac{{\partial u}} {{\partial t}} = \Delta {u^m}$, $ m > 1$, in the sense of distributions on $ D \times (0,T)$, and vanishes on $ \partial D \times (0,T)$ in a suitable weak sense, then $ u$ is Hölder continuous in $ \overline D \times (0,T)$.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1085940-6
Article copyright: © Copyright 1993 American Mathematical Society