We study a Hölder regularity of gradients for evolutional p-Laplacian systems with Hölder continuous coefficients and exterior force. We use the perturbation argument with the p-Laplacian systems with constant coefficients and only principal terms. The main task is to make the Hölder estimate of gradients for the systems above well-worked in the perturbation estimate. We also need to make a localization of the Hölder estimate in [2].
Mathematics Subject Classification (1991). 35D10, 35B65, 35K65
We study doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow from now on, which includes the classical Yamabe flow on a bounded domain in Euclidean space in the special case p = 2. In this article we establish a priori estimates and regularity results for the p-Sobolev type flow, which are necessary for further analysis and classification of limits as time tends to infinity.
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