Harnack inequalities and Hölder estimates for master equations

A. Biswas, M. De León-Contreras, P. R. Stinga

Published 2018-06-26Version 1

We show parabolic interior and boundary Harnack inequalities and local H\"older continuity for solutions to master equations of the form $(\partial_t+L)^su=f$ in $\mathbb{R}\times\Omega$, where $L$ is a divergence form elliptic operator and $\Omega\subseteq\mathbb{R}^n$. To this end, we prove that fractional powers of parabolic operators $\partial_t+L$ can be characterized with a degenerate parabolic extension problem.