منابع مشابه
Nodal Sets of Steklov
We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in Rn – the eigenfunctions of the Dirichlet-to-Neumann map Λ. For a bounded Lipschitz domain Ω ⊂ Rn, this map associates to each function u defined on the boundary ∂Ω, the normal derivative of the harmonic function on Ω with boundary data u. Under the assumption that the domain Ω is C2, we prove a do...
متن کاملNodal Length of Steklov Eigenfunctions on Real-analytic Riemannian Surfaces
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface as well as the construction of exponentially accurate approximations for the Steklov eigenfunctions near the boundary.
متن کاملOn the nodal sets of toral eigenfunctions
We study the nodal sets of eigenfunctions of the Laplacian on the standard d-dimensional flat torus. The question we address is: Can a fixed hypersurface lie on the nodal sets of eigenfunctions with arbitrarily large eigenvalue? In dimension two, we show that this happens only for segments of closed geodesics. In higher dimensions, certain cylindrical sets do lie on nodal sets corresponding to ...
متن کاملGeodesics and Nodal Sets of Laplace Eigenfunctions on Hyperbolic Manifolds
Let X be a manifold equipped with a complete Riemannian metric of constant negative curvature and finite volume. We demonstrate the finiteness of the collection of totally geodesic immersed hypersurfaces in X that lie in the zero-level set of an arbitrary Laplace eigenfunction. For surfaces, we show that the number can be bounded just in terms of the area of the surface. We also provide constru...
متن کاملA Geometric Covering Lemma and Nodal Sets of Eigenfunctions
The main purpose of this paper is two-fold. On one hand, we prove a sharper covering lemma in Euclidean space Rn for all n ≥ 2 (see Theorem 1.5). On the other hand, we apply this covering lemma to improve existing results for BMO and volume estimates of nodal sets for eigenfunctions u satisfying 4u + λu = 0 on n-dimensional Riemannian manifolds when λ is large (see Theorems 1.7, 1.8). We also i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2015
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-015-0864-8