Determination of second-order elliptic operators in two dimensions from partial Cauchy data
نویسندگان
چکیده
منابع مشابه
Determination of second-order elliptic operators in two dimensions from partial Cauchy data.
We consider the inverse boundary value problem in two dimensions of determining the coefficients of a general second-order elliptic operator from the Cauchy data measured on a nonempty arbitrary relatively open subset of the boundary. We give a complete characterization of the set of coefficients yielding the same partial Cauchy data. As a corollary we prove several uniqueness results in determ...
متن کاملPartial Cauchy Data for General Second Order Elliptic Operators in Two Dimensions
We consider the problem of determining the coefficients of a first-order perturbation of the Laplacian in two dimensions by measuring the corresponding Cauchy data on an arbitrary open subset of the boundary. From this information we obtain a coupled system of ∂z̄ and ∂z which the coefficients satisfy. As a corollary we show that for a simply connected domain we can determine uniquely the coeffi...
متن کاملGlobal Uniqueness from Partial Cauchy Data in Two Dimensions
We prove for a two dimensional bounded domain that the Cauchy data for the Schrödinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential. This implies, for the conductivity equation, that if we measure the current fluxes at the boundary on an arbitrary open subset of the boundary produced by voltage potentials supported in the same subset, we can de...
متن کاملOn a factorization of second order elliptic operators and applications
We show that given a nonvanishing particular solution of the equation (div p grad+q)u = 0, (1) the corresponding differential operator can be factorized into a product of two first order operators. The factorization allows us to reduce the equation (1) to a first order equation which in a two-dimensional case is the Vekua equation of a special form. Under quite general conditions on the coeffic...
متن کاملAbout the mass of certain second order elliptic operators
Let (M, g) be a closed Riemannian manifold of dimension n ≥ 3 and let f ∈ C∞(M), such that the operator Pf := ∆g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of Pf as the constant term in the expansion of the Green function of Pf at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n−2 4(n−1) sg, ...
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: Proceedings of the National Academy of Sciences
سال: 2010
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.1011681107