Abstract
We study existence and regularity properties of solutions to the singular $p$-Laplacian parabolic system in a bounded domain $\Omega$. The main purpose is to prove global $L^r(\varepsilon,T;L^q(\Omega))$, $\varepsilon\geq0$, integrability properties of the second spatial derivatives and of the time derivative of the solutions. Hence, for suitable $p$ and exponents $r$ and $q$, 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 $p>\frac{2n}{n+2}$.
Citation
F. Crispo. P. Maremonti. "Higher regularity of solutions to the singular $p$-Laplacean parabolic system." Adv. Differential Equations 18 (9/10) 849 - 894, September/October 2013. https://doi.org/10.57262/ade/1372777762
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