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Towards a constructive method to determine an L∞-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 L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.
Astala, Kari, and Päivärinta, Lassi. "A boundary integral equation for Calderón's inverse conductivity problem.." Collectanea Mathematica 57.Extra (2006): 127-139. <http://eudml.org/doc/41788>.
@article{Astala2006, abstract = {Towards a constructive method to determine an L∞-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 L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.}, author = {Astala, Kari, Päivärinta, Lassi}, journal = {Collectanea Mathematica}, keywords = {Ecuaciones diferenciales elípticas; Ecuaciones integrales; Problemas inversos; Operadores de Fredholm; boundary data; complex geometric optics solutions; Dirichlet to Neumann operator; Fredholm integral equation of the second kind}, language = {eng}, number = {Extra}, pages = {127-139}, title = {A boundary integral equation for Calderón's inverse conductivity problem.}, url = {http://eudml.org/doc/41788}, volume = {57}, year = {2006}, }
TY - JOUR AU - Astala, Kari AU - Päivärinta, Lassi TI - A boundary integral equation for Calderón's inverse conductivity problem. JO - Collectanea Mathematica PY - 2006 VL - 57 IS - Extra SP - 127 EP - 139 AB - Towards a constructive method to determine an L∞-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 L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body. LA - eng KW - Ecuaciones diferenciales elípticas; Ecuaciones integrales; Problemas inversos; Operadores de Fredholm; boundary data; complex geometric optics solutions; Dirichlet to Neumann operator; Fredholm integral equation of the second kind UR - http://eudml.org/doc/41788 ER -