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Transactions of the American Mathematical Society

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Weak solutions of the porous medium equation


Authors: Björn E. J. Dahlberg and Carlos E. Kenig
Journal: Trans. Amer. Math. Soc. 336 (1993), 711-725
MSC: Primary 35D05; Secondary 35K55, 76S05
DOI: https://doi.org/10.1090/S0002-9947-1993-1085939-X
MathSciNet review: 1085939
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Abstract: We show that if $ u \geq 0$, $ u \in L_{{\text{loc}}}^m(\Omega )$, $ \Omega \subset {{\mathbf{R}}^{n + 1}}$ solves $ \partial u/\partial t = \Delta {u^m}$, $ m > 1$ , in the sense of distributions, then $ u$ is locally Hölder continuous in $ \Omega $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1085939-X
Article copyright: © Copyright 1993 American Mathematical Society

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