Variational Solutions For Fractal Transmission Problems

The aim of this talk is to describe second order transmission problems involving a layer of fractal type, which is imbedded in an Euclidean domain. Fractals are geometric objects with highly non-Euclidean characteristics: despite their tricky geometry, there are however large families of fractals which possess a very rich analytic structure. So we are able to study fractals both as intrinsic bodies, in which is possible to give a suitable notion of Laplacean and as boundaries of Euclidean domains supporting traces of functions belonging to classic spaces like mains supporting traces of functions belonging to classic spaces like Sobolev spaces. Or possibly as bodies and boundaries at the same time, when they occur as highly conductive layers inside a Euclidean domain, which is the situation we focus on in this presentation.