Détection et approximation de défauts non-réguliers

This Note deals with the identifiability of non-smooth defects by boundary measurements. We prove the uniqueness of the detection by two measurements for arbitrary closed sets satisfying quasi-everywhere a conductivity assumption. This assumption is satisfied by a large class of compact sets, including all the sets which can be written as an arbitrary union of continua of positive diameter. The conductivity is a new regularity concept which is related to the thickness of the set and is to be compared to the Wiener regularity. In order to rigorously justify the numerical approach by the finite element method, we provide a stability result without any a priori smoothness assumptions. To cite this article: Z. Belhachmi, D. Bucur, C. R. Acad. Sci. Paris, Ser. I 340 (2005).