Elliptic Equations: Many Boundary Measurements
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Isakov V. (2017) Chapter 5. Elliptic Equations: Many Boundary Measurements. In: Inverse Problems for Partial Differential Equations. Applied Mathematical Sciences, vol 127. Springer, Cham, pp.149-210
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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