A boundary integral equation for Calderón's inverse conductivity problem

• Autores: Kari Astala , Lassi Päivärinta
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 57, Fasc. Extra 1, 2006 (Ejemplar dedicado a: Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations), págs. 126-139
• Idioma: español
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• Resumen

  • Towards a constructive method to determine an L1-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L1-conductivity problem can be determined in a stable manner at the boundary and outside of the body.

• Referencias bibliográficas
  • L.V. Ahlfors, Lectures on Quasiconformal Mappings, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced...
  • K. Astala and L. Päivärinta, Calderón’s inverse conductivity problem in the plane, Ann. of Math., to appear.
  • A.I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math. 143 (1996), 71–96.
  • A.I. Nachman, Reconstructions from boundary measurements, Ann. of Math. 128 (1988), 531–576.