15 citations · 30 across the 12 of their papers we have counts for
21 papers
Eigenfunction asymptotics and nodal domain estimates for dumbbell domains
Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola
We study the nodal structure of Neumann eigenfunctions on planar dumbbell domains as the width of the neck joining two fixed end domains tends to zero. Under simplicity and non-deg…
Nodal Deficiency of Neumann Eigenfunctions on a Symmetric Dumbbell Domain
Thomas Beck, Andrew Lyons
We study the nodal deficiency of pairs of Neumann eigenfunctions defined over symmetric dumbbell domains. As the width of the connecting neck shrinks, these eigenfunctions converge…
On non-local exchange and scattering operators in domain decomposition methods
Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola
We study non-local exchange and scattering operators arising in domain decomposition algorithms for solving elliptic problems on domains in . Motivated by recent form…
Two-phase problems: Perron solutions and regularity of the Neumann problem in convex cones
Thomas Beck, Daniela De Silva, Ovidiu Savin
We investigate a fully nonlinear two-phase free boundary problem with a Neumann boundary condition on the boundary of a general convex set with corners. We…
Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains
Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola
We obtain upper bounds on the number of nodal domains of Laplace eigenfunctions on chain domains with Neumann boundary conditions. The chain domains consist of a family of planar d…
Nodal Set Openings on Perturbed Rectangular Domains
Thomas Beck, Marichi Gupta, Jeremy L. Marzuola
We study the effects of perturbing the boundary of a rectangle on the nodal sets of eigenfunctions of the Laplacian. Namely, for a rectangle of a given aspect ratio , we identif…