Reconstruction of Small Inhomogeneities from Boundary Measurements, 1846. sayı
This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
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algorithm apply associated assume asymptotic expansion asymptotic formula background boundary bounded Lipschitz domain Chap chapter compact complete compute conclude condition conductivity consider constant contained corresponding defined definition denote depends derive Detection determine Dirichlet disk do(y elastic ellipse equation equivalent estimate example exists fact formula Fourier function give given GPT's harmonic hence holds identity imaging immediately inclusions independent inequality integral introduce invertible Lamé layer potentials Lemma linear Lipschitz character Lipschitz-continuous matrix measurements method Moreover Neumann Note Observe obtain operator pair polarization tensor positive present problem Proof properties prove reconstruction relation representation represented respectively satisfies single solution solving space Step Suppose symmetric takes term Theorem transform transmission unique unique solution values vector voltage yields zero ди