Regularity theory for nonlocal space-time master equations

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2020-01-01
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Biswas, Animesh
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Pablo R Stinga
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Altmetrics
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Mathematics
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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 semi-permeable 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. As a consequence, we obtain interior and boundary Harnack inequalities and sharp interior and global parabolic Schauder estimates for solutions. For the latter, we also prove a characterization of the correct intermediate parabolic Hölder spaces in the spirit of Sergio Campanato.

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Sat Aug 01 00:00:00 UTC 2020