The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary
نویسندگان
چکیده
منابع مشابه
The Inverse Problem for the Dirichlet-to-neumann Map on Lorentzian Manifolds
We consider the Dirichlet-to-Neumann map Λ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric g, a magnetic field A and a potential q. We show that we can recover the jet of g,A, q on the boundary from Λ up to a gauge transformation in a stable way. We also show that Λ recovers the following three invariants in a stable way: the lens relation of g, and the...
متن کاملDirichlet-to-Neumann Map Method with Boundary Cells for Photonic Crystals Devices
In a two-dimensional (2D) photonic crystal (PhC) composed of circular cylinders (dielectric rods or air holes) on a square or triangular lattice, various PhC devices can be created by removing or modifying some cylinders. Most existing numerical methods for PhC devices give rise to large sparse or smaller but dense linear systems, all of which are expensive to solve if the device is large. In a...
متن کاملThe generalised Dirichlet to Neumann map for moving initial-boundary value problems
We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectral analysis of an associated ODE...
متن کاملBoundary Determination of Conductivities and Riemannian Metrics via Local Dirichlet-to-Neumann Operator
We consider the inverse problem to identify an anisotropic conductivity from the Dirichlet-to-Neumann (DtN) map. We first find an explicit reconstruction of the boundary value of less regular anisotropic (transversally isotropic) conductivities and their derivatives. Based on the reconstruction formula, we prove Hölder stability, up to isometry, of the inverse problem using a local DtN map.
متن کاملDirichlet Duality and the Nonlinear Dirichlet Problem on Riemannian Manifolds
In this paper we study the Dirichlet problem for fully nonlinear secondorder equations on a riemannian manifold. As in our previous paper [HL4] we define equations via closed subsets of the 2-jet bundle where each equation has a natural dual equation. Basic existence and uniqueness theorems are established in a wide variety of settings. However, the emphasis is on starting with a constant coeff...
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: Communications in Analysis and Geometry
سال: 2003
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2003.v11.n2.a2