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We analyze the inverse problem of identifying the conductivity coefficient 1+ρ of the heat equation. We prove an uniqueness result for a linearized version this problem in Rn for n odd that does not depend on hypothesis about the relative position of the support of the unknown function ρ, assumed to be compact, with respect to a bounded open set Ω∗, where temperature measurements are taken. We proved a result in which supp(Ω) can be not simply connected, and Ω∗ can belong to one of its bounded connected components. It is an extension, for n odd, of a theorem proved by Elayyan and Isakov.

Um problema inverso de identificação do coeficiente de condutividade da equação do calor envolvendo regiões não simplesmente conexas