Elliptic Equations: Single Boundary Measurements

  • Victor Isakov
Part of the Applied Mathematical Sciences book series (AMS, volume 127)


In this chapter we consider the elliptic second-order differential equation \(Au = f\quad \mathrm{in}\;\varOmega,f = f_{0} -\sum \limits _{j=1}^{n}\partial _{j}f_{j}\) with the Dirichlet boundary data \(u = g_{0}\quad \mathrm{on}\;\partial \varOmega.\) We assume that A = div(−a∇) + b ⋅ ∇ + c with bounded and measurable coefficients a (symmetric real-valued (n × n) matrix) and complex-valued b and c in L (Ω). Another assumption is that A is an elliptic operator; i.e., there is ɛ0 > 0 such that a(x)ξ ⋅ ξ ≥ ɛ0 | ξ | 2 for any vector \(\xi \in \mathbb{R}^{n}\) and any x ∈ Ω. Unless specified otherwise, we assume that Ω is a bounded domain in \(\mathbb{R}^{n}\) with the boundary of class C2. However, most of the results are valid for Lipschitz boundaries.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Victor Isakov
    • 1
  1. 1.Department of Mathematics and StatisticsWichita State UniversityWichitaUSA

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