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
Copyright Date
2020-08
Language
en
File Format
application/pdf
File Size
138 pages
Recommended Citation
Biswas, Animesh, "Regularity theory for nonlocal space-time master equations" (2020). Graduate Theses and Dissertations. 18099.
https://lib.dr.iastate.edu/etd/18099
