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The regularity for nonlinear parabolic systems of p-Laplacian type with critical growth |
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| Authors: | Chiara Leone Masashi Misawa Anna Verde |
| Institution: | 1. Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, Via Cintia, 80126 Naples, Italy;2. Department of Mathematics, Faculty of Sciences, Kumamoto University, 2-39-1 Kurokami, Kumamoto-shi, Kumamoto 860-8555, Japan |
| Abstract: | We study the Hölder regularity of weak solutions to the evolutionary p -Laplacian system with critical growth on the gradient. We establish a natural criterion for proving that a small solution and its gradient are locally Hölder continuous almost everywhere. Actually our regularity result recovers the classical result in the case p=2 16] and can be applied to study the regularity of the heat flow for m-dimensional H-systems as well as the m-harmonic flow. |
| Keywords: | primary 35D10 secondary 35D05 35B65 35K50 35K65 |
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