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.
A transmission problem on a polygonal partition: regularity and shape differentiability / Elena Beretta, Elisa Francini, Sergio Vessella. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - STAMPA. - 98:(2019), pp. 1862-1874. [10.1080/00036811.2018.1469012]
A transmission problem on a polygonal partition: regularity and shape differentiability
Elisa Francini
;Sergio Vessella
2019
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.
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