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September/October 2013 Higher regularity of solutions to the singular $p$-Laplacean parabolic system
F. Crispo, P. Maremonti
Adv. Differential Equations 18(9/10): 849-894 (September/October 2013).

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

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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.

Information

Published: September/October 2013
First available in Project Euclid: 2 July 2013

zbMATH: 1275.35053
MathSciNet: MR3100054

Subjects:
Primary: 35B65, 35K51, 35K67

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 9/10 • September/October 2013
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