Inverse Problems for Elliptic Equations in the Plane

Inverse Problems for Elliptic Equations in the Plane

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Description

This book provides mathematicians, physicists, and researchers in medical imaging with an in-depth study of geometrical properties of solutions of elliptic equations. This book introduces current research on inverse problems with a focus on aquifer identification and electrical impedance tomography. It restricts coverage to the two-dimensional case, which is a practical starting point for related investigations in higher dimensions. It presents applications and addresses different aspects of the conductivity problem. It also includes the theory of geometrical properties of solutions of elliptic equations in dimension two.show more

Product details

  • Hardback | 192 pages
  • 152 x 229mm
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • United States
  • English
  • 1584882859
  • 9781584882855

Table of contents

Introduction. Ill-posed Problems. Aquifer Identification, the Prospection of the Ground Transmissivity from Piezometric Head Measurements. Electrical Conductors and the Inverse Conductivity Problem. Divergence Structure Elliptic Equations in Two Variables and Geometric Properties of Solutions. Uniqueness and Stability for Aquifer Identification. The Detection of a Cavity in a Conductor. The Detection of Cracks in a Conductor. Results for the Inverse Problem of Detection of an Inclusion in a Conductor. References.show more