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Register a new userUnique recovery of piecewise analytic density and stiffness tensor from the elastic-wave Dirichlet-to-Neumann map
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We study the recovery of piecewise analytic density and stiffness tensor of a three-dimensional domain from the local dynamical Dirichlet-to-Neumann map. We give global uniqueness results if the medium is transversely isotropic with known axis of symmetry or orthorhombic with known symmetry planes on each subdomain. We also obtain uniqueness of a fully anisotropic stiffness tensor, assuming that it is piecewise constant and that the interfaces which separate the subdomains have curved portions. The domain partition need not to be known. Precisely, we show that a domain partition consisting of subanalytic sets is simultaneously uniquely determined.
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It was recently shown that the nodal deficiency of an eigenfunction is encoded in the spectrum of the Dirichlet-to-Neumann operators for the eigenfunctions positive and negative nodal domains. While originally derived using symplectic methods, this result can also be understood through the spectral flow for a family of boundary conditions imposed on the nodal set, or, equivalently, a family of operators with delta function potentials supported on the nodal set. In this paper we explicitly describe this flow for a Schrodinger operator with separable potential on a rectangular domain, and determine a mechanism by which lower energy eigenfunctions do or do not contribute to the nodal deficiency.
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