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Publication Cover
Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 10
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Articles

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

Elena BerettaDipartimento di Matematica “Brioschi”, Politecnico di Milano, Milano, Italy.View further author information
,
Elisa FranciniDipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Firenze, Italy.Correspondence[email protected]
View further author information
&
Sergio VessellaDipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Firenze, Italy.View further author information
Pages 1862-1874 | Received 27 Jan 2018, Accepted 17 Apr 2018, Published online: 02 May 2018
 
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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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Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Università degli Studi di Firenze [Fondi di ateneo 2017].

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