3 papers
math.AP2022
A strange term coming from the boundary data
Aaron Pim
In this paper, I derive the limiting behaviour of the solutions to Poisson's equation, in a perforated domain, subject to inhomogeneous Robin boundary conditions. In the first half…
math.AP2021
Asymptotic analysis of harmonic functions in singular domains with inhomogenous Robin boundary conditions
Aaron Pim, Kirill Cherednichenko, Jey Sivaloganathan
In 1991, Vladimir Maz'ya, Serguei Nazarov and Boris Plamenevskij developed the theory of compound asymptotics for elliptic boundary value problems in singularly perturbed domains.…
math.AP2021
A generalisation of the Poincaré-Hopf Theorem
Aaron Pim
The Poincaré-Hopf Theorem is a conservation law for real-analytic vector fields, which are tangential to a closed surface (such as a torus or a sphere). The theorem also governs re…