| Abstract: |
| We study the local H\{o}lder continuity of nonnegative solutions to the doubly nonlinear parabolic equation
\begin{equation*}
u_t-\textrm{div} \big(|Du^m|^{p-2} Du^m \big)=0
\end{equation*}
in the mixed degenerate-singular cases, up to certain Barenblat numbers:
\begin{equation*}
01,\quad \frac{2N}{N+1} |
|