Mary Vaughan
Ph.D.
Department of Mathematics and Statistics
The University of Western Australia
Research Interests: Partial Differential Equations and Harmonic Analysis
Nonlocal equations
Fractional derivatives
Fractional Laplacians
Fractional Allen-Cahn
Regularity theory
Harnack inequalities
Continuous Steiner symmetrizations
Peridynamics
List of Publications
You can find all my papers and preprints on ArXiv .
One-sided fractional derivatives, fractional Laplacians, and weighted Sobolev spaces ,
Nonlinear Anal. (2020) (with P. R. Stinga).
The dual Kaczmarz algorithm ,
Acta Appl Math. (2020) (with A. Aboud, E. Curl, S. N. Harding, and E. S. Weber).
Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality ,
J. Math. Pures Appl. (2021) (with P. R. Stinga).
Multiple interphases for fractional Allen-Cahn equations ,
preprint (2022) (with S. Patrizi).
Continuous symmetrizations and uniqueness of solutions to nonlocal equations ,
preprint (2023) (with M. G. Delgadino).
Interior Schauder estimates for fractional elliptic equations in nondivergence form ,
preprint (2024) (with P. R. Stinga).
Ph.D. Thesis : Here is a link to my dissertation.
Video Presentations
Research Training:
In 2018, I was one of twenty students selected to participate in the NSF Mathematical Sciences Graduate Internship .
I interned at Oak Ridge National Laboratory under the direction of Pablo Seleson .
When referring to the n th order derivative dn u(t)/dtn , L'Höpital asked Leibniz in his 1965 letter
"What if n is 1/2?"
Leibniz replied
"It will lead to a paradox. From this apparent paradox,
one day useful consequences will be drawn."