The study establishes local Hölder regularity for gradient in weak solutions of nonlinear parabolic systems, indicating implications for diffusion models.
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.
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Bögelein et al. (2026) studied this question.
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