A transmission problem on a polygonal partition: regularity and shape differentiability. Issue 10 (27th July 2019) - Beretta, Elena; Francini, Elisa; Vessella, Sergio
ABSTRACT: We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes of the partition. This allows to prove shape differentiability of solutions and to establish an explicit formula for the shape derivative.