Degree Type

Dissertation

Date of Award

2020

Degree Name

Doctor of Philosophy

Department

Mathematics

Major

Mathematics

First Advisor

Pablo R Stinga

Abstract

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.

DOI

https://doi.org/10.31274/etd-20200902-18

Copyright Owner

Animesh Biswas

Language

en

File Format

application/pdf

File Size

138 pages

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