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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asymptotic expansion asymptotic formula background solution boundary measurements bounded domain bounded Lipschitz domain Chap compact operators completes the proof compute conductivity inclusions constant C depending Corollary corresponding da(y defined denote derive Detection Dirichlet problem disk displacement vector dv dv eigenvalues elastic moment tensors electromagnetic inclusions ellipse EMT's equivalent ellipse estimate exists a constant fact finite number following theorem fundamental solution given GPT's Green's formula Green's function harmonic function harmonic polynomial Helmholtz equation hence holds holomorphic inequality integral equation invertible JdB JdB JdB ov Lame constants Lame system Lipschitz boundary Lipschitz character Lipschitz-continuous matrix modulo multi-index Neumann problem Observe orthonormal basis polarization tensor positive constant prove quadratic radius representation formula satisfies small inclusions Suppose symmetric tensor of Polya-Szego transmission problem unique solution vector Vogelius voltage potential zero