Abstract We establish the local Hölder regularity of the spatial gradient of bounded weak solutions to the nonlinear system of parabolic type where , , and the coefficient is bounded below by a positive constant and is Hölder continuous in the space variable . As an application, we prove Hölder estimates for the gradient of weak solutions to a doubly nonlinear parabolic equation in the supercritical fast diffusion regime.
Bögelein et al. (Sun,) studied this question.
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