Sam Farrington's Outputs (2)

On the Isoperimetric and Isodiametric Inequalities and the Minimisation of Eigenvalues of the Laplacian (2025)
Journal Article
Farrington, S. (2025). On the Isoperimetric and Isodiametric Inequalities and the Minimisation of Eigenvalues of the Laplacian. Journal of Geometric Analysis, 35(2), Article 62. https://doi.org/10.1007/s12220-024-01887-0

We consider the problem of minimising the k-th eigenvalue of the Laplacian with some prescribed boundary condition over collections of convex domains of prescribed perimeter or diameter. It is known that these minimisation problems are well-posed for... Read More about On the Isoperimetric and Isodiametric Inequalities and the Minimisation of Eigenvalues of the Laplacian.

Heat Flow in Polygons with Reflecting Edges (2023)
Journal Article
Farrington, S., & Gittins, K. (2023). Heat Flow in Polygons with Reflecting Edges. Integral Equations and Operator Theory, 95(4), Article 27. https://doi.org/10.1007/s00020-023-02749-0

We investigate the heat flow in an open, bounded set D in R2 with polygonal boundary ∂D. We suppose that D contains an open, bounded set D~ with polygonal boundary ∂D~. The initial condition is the indicator function of D~ and we impose a Neumann bou... Read More about Heat Flow in Polygons with Reflecting Edges.