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arXiv · 1801.09396

A transmission problem on a polygonal partition: regularity and shape differentiability

Elena Beretta·Elisa Francini·Sergio Vessella
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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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Elena Beretta, Elisa Francini, Sergio Vessella. 2018-01-29. A transmission problem on a polygonal partition: regularity and shape differentiability. https://doi.org/10.1080/00036811.2018.1469012

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