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Proceedings of the American Mathematical Society

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


Author: Teresa Isernia
Journal: Proc. Amer. Math. Soc. 146 (2018), 4741-4753
MSC (2010): Primary 35B65, 49N60, 35K40, 46E30
DOI: https://doi.org/10.1090/proc/14099
Published electronically: August 10, 2018
MathSciNet review: 3856142
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Abstract: We prove the local boundedness of weak solutions for the following non-linear second order parabolic systems:

$\displaystyle u_{t} - \textup {div} \left ( \frac {\mathcal {\varphi }'(\vert Du\vert)}{\vert Du\vert}Du\right )=0$$\displaystyle \mbox { in } \Omega _{T}:=\Omega \times (-T,0),$    

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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Additional Information

Teresa Isernia
Affiliation: Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 12, 60131 Ancona, Italy
Email: teresa.isernia@unina.it

DOI: https://doi.org/10.1090/proc/14099
Keywords: $\mathcal{\varphi}$-caloric functions, parabolic systems, Moser iteration, general growth
Received by editor(s): July 24, 2017
Received by editor(s) in revised form: January 16, 2018
Published electronically: August 10, 2018
Communicated by: Joachim Krieger
Article copyright: © Copyright 2018 American Mathematical Society