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.
2019
98
1862
1874
Elena Beretta, Elisa Francini, Sergio Vessella
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1127132
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