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Global higher integrability of weak solutions of porous medium systems

  • * Corresponding author

    * Corresponding author 

K. Moring has been supported by the Magnus Ehrnrooth foundation. T. Singer has been supported by the DFG-Project SI 2464/1-1 ``Highly nonlinear evolutionary problems"

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  • We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by

    $ \begin{equation*} \partial_t u-\Delta(|u|^{m-1}u) = \mathrm{div}\,F\,, \end{equation*} $

    where $ m>1 $. More precisely, we prove that under suitable assumptions the spatial gradient $ D(|u|^{m-1}u) $ of any weak solution is integrable to a larger power than the natural power $ 2 $. Our analysis includes both the case of the lateral boundary and the initial boundary.

    Mathematics Subject Classification: 35B65, 35K65, 35K40, 35K55.


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