Chapter 5 -- Elliptic Equations: Many Boundary Measurements

Abstract

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.