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In [2], A. P. Caldkron posed the following question: can one determine the heat conductivity of an object from static temperature and heat flux measurements at the boundary? We show that such measurements uniquely determine the conductivity and all of its derivatives at the boundary.One wants, for various applications, to determine the internal structure of an object by means of measurements at the boundary. We study an inverse problem of this type which was raised by A. P. Caldkron in [2].Let R be a bounded C" domain in R", n h 2, with boundary r. For any Cald6ron showed that Q, is analytic as a function of y E L", and that the differential d@)y=constant is injective. He also gave a method for approximating y using knowledge of O,, in case y is nearly constant and sufficiently smooth. The analysis in [2] does not show, however, that Q, is injective, even in a neighborhood of y = constant.We shall prove that O, determines y and all its derivatives at the boundary, provided y is smooth near the boundary.

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