43 citations · 106 across the 34 of their papers we have counts for
6 papers · 1 filter
Extremal domains and Pólya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles
Pedro Freitas, James Kennedy
We show that eigenvalues of the Robin Laplacian with a positive boundary parameter on rectangles and unions of rectangtes satisfy Pólya-type inequalities, albeit with an expone…
The spectrum of geodesic balls on spherically symmetric manifolds
Denis Borisov, Pedro Freitas
We study the Dirichlet spectrum of the Laplace operator on geodesic balls centred at a pole of spherically symmetric manifolds. We first derive a Hadamard--type formula for the dep…
On the spectrum of deformations of compact double-sided flat hypersurfaces
Denis Borisov, Pedro Freitas
We study the asymptotic behaviour of the eigenvalues of the Laplace-Beltrami operator on a compact hypersurface in \mathds{R}^{n+1} as it is flattened into a singular double-sided…
Asymptotics for the expected lifetime of Brownian motion on thin domains in R^n
Denis Borisov, Pedro Freitas
We derive a three-term asymptotic expansion for the expected lifetime of Brownian motion and for the torsional rigidity on thin domains in R^n, and a two-term expansion for the max…
Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in R^d
Denis Borisov, Pedro Freitas
We consider the Laplace operator with Dirichlet boundary conditions on a domain in R^d and study the effect that performing a scaling in one direction has on the eigenvalues and co…
Characterization of harmonic and subharmonic functions via mean-value properties
Pedro Freitas, Joao Palhoto Matos
We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for…