The inverse Calderón problem, ill-posedness and remedies
Giovanni Alessandrini, Università degli Studi di Trieste
11 de Enero 2013, Aula Azul ICMAT, 12:00 h.
(Calle Nicolás Cabrera, 15, Campus de Cantoblanco)
Abstract. This talk is devoted to some aspects of the nonlinear inverse problem of Calderòn, that is to determine the internal electrical conductivity of a body from boundary measurements of voltage and current. Or, in other words, to determine the leading coefficient in an elliptic equation from the Cauchy data of all of its solutions. I shall discuss the fact that this problem is not well-posed in the sense of Hadamard, by showing some examples and by outlining some connections with the prototypical (linear) ill-posed problem: the Cauchy problem for elliptic equations. Finally I shall illustrate some of the strategies that have been devised in order to cope with such ill-posedness.