Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions
نویسندگان
چکیده
منابع مشابه
A new approach to analyticity of Dirichlet-Neumann operators
This paper outlines the theoretical background of a new approach towards an accurate and well-conditioned perturbative calculation of Dirichlet{Neumann operators (DNOs) on domains that are perturbations of simple geometries. Previous work on the analyticity of DNOs has produced formulae that, as we have found, are very ill-conditioned. We show how a simple change of variables can lead to recurs...
متن کاملAnalyticity of Dirichlet-Neumann Operators on Hölder and Lipschitz Domains
In this paper we take up the question of analyticity properties of Dirichlet–Neumann operators with respect to boundary deformations. In two separate results, we show that if the deformation is sufficiently small and lies either in the class of C1+α (any α > 0) or Lipschitz functions, then the Dirichlet–Neumann operator is analytic with respect to this deformation. The proofs of both results ut...
متن کاملFriedlander’s Eigenvalue Inequalities and the Dirichlet-to-neumann Semigroup
If Ω is any compact Lipschitz domain, possibly in a Riemannian manifold, with boundary Γ = ∂Ω, the Dirichlet-to-Neumann operator Dλ is defined on L2(Γ) for any real λ. We prove a close relationship between the eigenvalues of Dλ and those of the Robin Laplacian ∆μ, i.e. the Laplacian with Robin boundary conditions ∂νu = μu. This is used to give another proof of the Friedlander inequalities betwe...
متن کاملThe domain of analyticity of Dirichlet–Neumann operators
Dirichlet–Neumann operators arise in many applications in the sciences, and this has inspired a number of studies on their analytical properties. In this paper we further investigate the analyticity properties of Dirichlet–Neumann operators as functions of the boundary shape. In particular, we study the size of the disc of convergence of their Taylor-series representation. For this we use a com...
متن کاملDirichlet-to-Neumann semigroup acts as a magnifying glass
The first aim of this paper is to illustrate numerically that the Dirichlet-to-Neumann semigroup represented by P. Lax acts as a magnifying glass. In this perspective, we used the finite element method for the discretization of the correspondent boundary dynamical system using the implicit and explicit Euler schemes. We prove by using the Chernoff’s Theorem that the implicit and explicit Euler ...
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: Journal of Evolution Equations
سال: 2018
ISSN: 1424-3199,1424-3202
DOI: 10.1007/s00028-018-0467-x