Verena Bögelein, Frank Duzaar, Ugo Gianazza, Naian Liao, Christoph Scheven
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.