Inverse Problems for Elliptic Equations

Alemdar Hasanov Hasanoğlu and Vladimir G. Romanov
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Alemdar Hasanov Hasanoğlu: University of Kocaeli, Department of Mathematics
Vladimir G. Romanov: Sobolev Institute of Mathematics

Chapter Chapter 7 in Introduction to Inverse Problems for Differential Equations, 2021, pp 213-226 from Springer

Abstract: Abstract This chapter is an introduction to the basic inverse problems for elliptic equations. One class of these inverse problems arises when the Born approximation is used for scattering problem in quantum mechanics, acoustics or electrodynamics. In the first part of this chapter two inverse problems, the inverse scattering problem at a fixed energy and the inverse scattering problems at a fixed energy, are studied. The last problem is reduced to the tomography problem which is studied in the next chapter. In the second part of the chapter, the Dirichlet-to-Neumann operator is introduced. It is proved that this operator uniquely defines the potential q(x) in Δu(x) + q(x) = 0.

Date: 2021
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DOI: 10.1007/978-3-030-79427-9_7

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