43 citations · 106 across the 34 of their papers we have counts for
Showing 2007Show all
3 papers · 1 filter
math.SP2007★ 1 cited
Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains
Denis Borisov, Pedro Freitas
We consider the Laplace operator with Dirichlet boundary conditions on a planar domain and study the effect that performing a scaling in one direction has on the spectrum. We deriv…
math.SP2007★ 1 cited
A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains
Pedro Freitas, David Krejcirik
We show that as the ratio between the first Dirichlet eigenvalues of a convex domain and of the ball with the same volume becomes large, the same must happen to the corresponding r…
math-ph2007★ 16 cited
Waveguides with combined Dirichlet and Robin boundary conditions
Pedro Freitas, David Krejcirik
We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variabl…