October 12, 2021

Regularity Estimate for Nonlocal Space-Time Master Equations

We analyze regularity estimates for solutions to nonlocal space-time equations driven by fractional powers of parabolic operators in divergence form. These equations are fundamental in semipermeable membrane problems, biological invasion models and they also appear as generalized Master equations. We develop a parabolic method of semigroups that allows us to prove a local extension problem characterization for these nonlocal problems.

In this talk, we will discuss how we obtained Harnack inequalities and Schauder estimates for the solutions using the extension method.

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