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Some recent developments on the Steklov eigenvalue problem
The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of
interest in the past few decades. This article is a tour of some of the recent developments …
interest in the past few decades. This article is a tour of some of the recent developments …
The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript
How close is the Dirichlet-to-Neumann (DtN) map to the square root of the corresponding
boundary Laplacian? This question has been actively investigated in recent years …
boundary Laplacian? This question has been actively investigated in recent years …
A numerical study of the generalized Steklov problem in planar domains
We numerically investigate the generalized Steklov problem for the modified Helmholtz
equation and focus on the relation between its spectrum and the geometric structure of the …
equation and focus on the relation between its spectrum and the geometric structure of the …
Robust superlinear Krylov convergence for complex noncoercive compact-equivalent operator preconditioners
Preconditioning for Krylov methods often relies on operator theory when mesh independent
estimates are looked for. The goal of this paper is to contribute to the long development of …
estimates are looked for. The goal of this paper is to contribute to the long development of …
A numerical study of the Dirichlet-to-Neumann operator in planar domains
We numerically investigate the generalized Steklov problem for the modified Helmholtz
equation and focus on the relation between its spectrum and the geometric structure of the …
equation and focus on the relation between its spectrum and the geometric structure of the …
The Steklov problem for exterior domains: asymptotic behavior and applications
We investigate the spectral properties of the Steklov problem for the modified Helmholtz
equation $(p-\Delta) u= 0$ in the exterior of a compact set, for which the positive parameter …
equation $(p-\Delta) u= 0$ in the exterior of a compact set, for which the positive parameter …
[HTML][HTML] Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces
T Arias-Marco, EB Dryden, CS Gordon… - Journal of Mathematical …, 2024 - Elsevier
We consider three different questions related to the Steklov and mixed Steklov problems on
surfaces. These questions are connected by the techniques that we use to study them, which …
surfaces. These questions are connected by the techniques that we use to study them, which …
Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues
In the present paper we develop an approach to obtain sharp spectral asymptotics for
Steklov type problems on planar domains with corners. Our main focus is on the two …
Steklov type problems on planar domains with corners. Our main focus is on the two …
Sloshing, Steklov and corners: asymptotics of sloshing eigenvalues
In the present paper we develop an approach to obtain sharp spectral asymptotics for
Steklov type problems on planar domains with corners. Our main focus is on the two …
Steklov type problems on planar domains with corners. Our main focus is on the two …
Mixed Steklov-Neumann problem: asymptotic analysis and applications to diffusion-controlled reactions
DS Grebenkov - arxiv preprint arxiv:2409.00213, 2024 - arxiv.org
Many first-passage processes in complex media and related diffusion-controlled reactions
can be described by means of eigenfunctions of the mixed Steklov-Neumann problem. In …
can be described by means of eigenfunctions of the mixed Steklov-Neumann problem. In …