A transmission problem on a polygonal partition: regularity and shape differentiability |
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| Authors: | Elena Beretta Sergio Vessella |
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| Affiliation: | 1. Dipartimento di Matematica “Brioschi”, Politecnico di Milano, Milano, Italy.;2. Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Firenze, Italy. |
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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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| Keywords: | Polygonal inclusions conductivity equation shape derivative |
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