Hölder regularity of the gradient for the non-homogeneous parabolic \(p(x,t)\)-Laplacian equations (Q2922237)

In this paper, the author obtains the local Hölder regularity of the gradient of weak solutions for the non-homogeneous parabolic \(p(x,t)\)-Laplacian equation NEWLINE\[NEWLINE u_t-\text{div}((A\nabla u\cdot\nabla u)^{\frac{p(x)-2}{2}}A\nabla u)=\text{div}(|f|^{p(x)-2}f), NEWLINE\]NEWLINE provided \(p(x,t), A\) and \(f\) are Hölder-continuous functions.