On the Hölder Regularity of Signed Solutions to a Doubly Nonlinear Equation. Part III

Abstract

AbstractWe establish the local Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is $$ \begin{align*} & \partial_t\big(|u|^{q-1}u\big)-\Delta_p u=0,\quad 1<p<2,\quad 0<p-1<q. \end{align*}$$The proof exploits the space expansion of positivity for the singular, parabolic $p$-Laplacian and employs the method of intrinsic scaling by carefully balancing the double singularity.