Partial gradient regularity for parabolic systems with degenerate diffusion and Hölder continuous coefficients
Fabian Bäuerlein · Nonlinear Analysis · 2024
We consider vector valued weak solutions ?? ∶ ???? R?? with ?? ∈ N of degenerate or singularparabolic systems of type?????? − div ??(??, ??, ????) = 0 in ???? = ?? × (0, ?? ),where ?? denotes an open set in R?? for ?? ≥ 1 and ?? > 0 a finite time. Assuming that the vectorfield ?? is not of Uhlenbeck-type structure, satisfies ??-growth assumptions and (??, ??) ↦ ??(??, ??, ??)is Hölder continuous for every ?? ∈ R?? ??, we show that the gradient ???? is partially Höldercontinuous, provided the vector field degenerates like that of the ??-Laplacian for small gradients.