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July/August 2015 Hölder regularity for singular parabolic systems of $p$-Laplacian type
Corina Karim, Masashi Misawa
Adv. Differential Equations 20(7/8): 741-772 (July/August 2015). DOI: 10.57262/ade/1431115715

Abstract

We study the regularity for nonlinear parabolic systems of $p$-Laplacian type, in the singular case $\frac{{2m}}{{m + 2}}<p<2$. We show an optimal condition on given external forces for a local Höolder continuity. Actually, our main result recovers the classical one for linear equations. The proof is based on Campanato's direct approach with the intrinsic scaling to the evolutionary $p$-Laplace operator. The iteration scheme is performed similarly as in [18], however, with some technical care peculiar to the singular case.

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Corina Karim. Masashi Misawa. "Hölder regularity for singular parabolic systems of $p$-Laplacian type." Adv. Differential Equations 20 (7/8) 741 - 772, July/August 2015. https://doi.org/10.57262/ade/1431115715

Information

Published: July/August 2015
First available in Project Euclid: 8 May 2015

zbMATH: 1327.35228
MathSciNet: MR3344617
Digital Object Identifier: 10.57262/ade/1431115715

Subjects:
Primary: 35B65 , 35D30 , 35K67

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 7/8 • July/August 2015
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