Hugo Fellows-Smith
Regularity of solutions to elliptic boundary value problems near cusp domain boundaries
“We will study the behaviour of solutions to elliptic PDE boundary value problems such as the shape of a domain’s boundary is deformed to a cusp.
The project will begin with a thorough revision of classical results of PDE theory on existence/uniqueness of solutions to boundary value problems on suitable spaces of functions, followed by a study of the trace operator and attempts to find explicit trace operators for some prototype examples of cusp boundaries.
We hope to apply what we learn with simpler elliptic equations such as Poisson’s equation to the Grad-Shafranov equation with a heart-shaped boundary.”
Hugo Fellows-Smith
The University of Western Australia
Before commencing his undergraduate studies in Mathematics at the University of Western Australia, Hugo Fellows-Smith was planning to major in philosophy. It was only after attending a summer school hosted by MAWA that he re-ignited his passion for mathematics and made the last-minute decision to study mathematics full-time! He has found immense pleasure in his studies, with a particular enjoyment of partial differential equations, and complex analysis. He wants to learn more about calculus of variations, calculus on manifolds, complex systems, random processes, and stochastic differential equations.
Hugo is most interested in “dreaming big” with mathematics. He enjoys thinking about mathematical objects that are very information dense, and loves how it feels to make mathematical abstractions.
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