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arXiv · 1209.1038

Higher regularity of solutions to the singular p-Laplacean parabolic system

Francesca Crispo·Paolo Maremonti
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Abstract

We study existence and regularity properties of solutions to the singular $p$-Laplacean parabolic system in a bounded domain $Ω$. The main purpose is to prove global $L^r(\varepsilon,T;L^q(Ω))$, $\varepsilon\geq0$, integrability properties of the second spatial derivatives and of the time derivative of the solutions. Hence, for suitable $p$ and exponents $r,\,q$, by Sobolev embedding theorems, we deduce global regularity of $u$ and $\nabla u$ in Hölder spaces. Finally we prove a global pointwise bound for the solution under the assumption $p>\frac{2n}{n+2}$.

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Francesca Crispo, Paolo Maremonti. 2012-09-05. Higher regularity of solutions to the singular p-Laplacean parabolic system. https://arxiv.org/abs/1209.1038

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