Abstract:The aim of this paper is to study the solvability of the problemwhere is a bounded smooth domain of R N , N > 2s, M 2 f0; 1g, 0 < s < 1, > 0, > 0, p > 1 and f is a nonnegative function. We distinguish two cases: -For M D 0, we prove the existence of a solution for every > 0 and > 0.-For M D 1, we consider f Á 1 and we find a threshold ƒ such that there exists a solution for every 0 < < ƒ, and there does not for > ƒ. To Daniela Giachetti, in occasion of her 60th birthday, with our friendship.

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We prove existence and homogenization results for a family of elliptic problems involving interfaces and a singular lower order term. These problems model heat or electrical conduction in composite media.

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