Corina Karim, Masashi Misawa, Yoshikazu Giga
We study the regularity for nonlinear parabolic systems of p-Laplacian type, in the singular case 2m/m+2 < p < 2. We show an optimal condition on given external forces for a local Hölder 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.
Departement of Mathematics, Graduate School of Science, Technology Kumamoto University, 2-39-1 Kurokami, Kumamoto-shi Kumamoto, 80-8555, Japan; Departement of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Veteran, Malang, 65145, Indonesia
