Advances in Differential Equations

Hölder regularity for singular parabolic systems of $p$-Laplacian type

Corina Karim and Masashi Misawa

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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.

Article information

Adv. Differential Equations, Volume 20, Number 7/8 (2015), 741-772.

First available in Project Euclid: 8 May 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35D30: Weak solutions 35B65: Smoothness and regularity of solutions 35K67: Singular parabolic equations


Karim, Corina; Misawa, Masashi. Hölder regularity for singular parabolic systems of $p$-Laplacian type. Adv. Differential Equations 20 (2015), no. 7/8, 741--772.

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