𝐿^{∞}-regularity for a wide class of parabolic systems with general growth

Isernia, Teresa

doi:10.1090/proc/14099

$L^{\infty }$-regularity for a wide class of parabolic systems with general growth
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by Teresa Isernia PDF

Proc. Amer. Math. Soc. 146 (2018), 4741-4753 Request permission

Abstract:

We prove the local boundedness of weak solutions for the following non-linear second order parabolic systems: \begin{equation*} u_{t} - \mathrm {div} \left ( \frac {\mathcal {\varphi }’(|Du|)}{|Du|}Du\right )=0 \mbox { in } \Omega _{T}:=\Omega \times (-T,0), \end{equation*} where $\Omega \subset \mathbb {R}^{n}$ is a bounded domain and $\mathcal {\varphi }$ is a given $N$-function. The proof of this result is based on a Moser-type iteration argument.

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