منابع مشابه
Asymptotics of Eigenfunctions on Plane Domains
We consider a family of domains (ΩN )N>0 obtained by attaching an N×1 rectangle to a fixed set Ω0 = {(x, y) : 0 < y < 1, −φ(y) < x < 0}, for a Lipschitz function φ ≥ 0. We derive full asymptotic expansions, as N → ∞, for the mth Dirichlet eigenvalue (for any fixed m ∈ N) and for the associated eigenfunction on ΩN . The second term involves a scattering phase arising in the Dirichlet problem on ...
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— The paper présents a gênerai discretization method for convective diffusion équations. The schemes are hased on an intégral formula and have the following advantages : 1. They are effective particularly in the case when convection is dominated ; 2. Solutions obtained by them satisfy a discrete conservation law ; 3. A discrete maximum principle is valid. We show that the fïnite element solutio...
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Any isospectral family of two-dimensional Euclidean domains is shown to be compact in the C(infinity) topology. Previously Melrose, using heat invariants, was able to establish the C(infinity) compactness of the curvature of the boundary curves. The additional ingredient used in this paper to obtain the compactness of the domains is the behavior of the determinant of the Laplacian near the boun...
متن کاملPositive Harmonic Functions on Denjoy Domains in the Complex Plane
Let Ω be a domain in the complex plane C whose complement E = C \ Ω, where C = C ∪ {∞} is a subset of the real line (i.e. Ω is a Denjoy domain). If each point of E is regular for the Dirichlet problem in Ω, we provide a geometric description of the structure of E near infinity such that the Martin boundary of Ω has one or two “infinite” points.
متن کاملA Generalized Hyperbolic Metric for Plane Domains
A plane domain Ω with more than one boundary point admits a hyperbolic metric and with respect to this metric, every holomorphic map of Ω into a subdomain X ⊆ Ω is a contraction. In this paper we define a new metric for the image domain X that is greater than or equal to the hyperbolic metric. Like the hyperbolic metric it has the property that any holomorphic map from Ω into X is a contraction...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1976
ISSN: 0386-5991
DOI: 10.2996/kmj/1138847328