Chapter 5 -- Elliptic Equations: Many Boundary Measurements
Isakov, Victor, 1947-
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Isakov V. (2017) Elliptic Equations: Many Boundary Measurements. In: Inverse Problems for Partial Differential Equations. Applied Mathematical Sciences, vol 127. Springer, Cham
We consider the Dirichlet problem (4.0.1), (4.0.2). At first we assume that for any Dirichlet data g0 we are given the Neumann data g1; in other words, we know the results of all possible boundary measurements, or the so-called Dirichlet-to-Neumann operator Λ:H1/2(∂Ω)→H−1/2(∂Ω)Λ:H1/2(∂Ω)→H−1/2(∂Ω), which maps the Dirichlet data g0 into the Neumann data g1.
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