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

Elena Beretta; Elisa Francini; Sergio Vessella

doi:10.1080/00036811.2018.1469012

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

Elena Beretta, Elisa Francini, Sergio Vessella

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	1862-1874
Number of pages	13
Journal	Applicable Analysis
Volume	98
Issue number	10
DOIs	https://doi.org/10.1080/00036811.2018.1469012
State	Published - Jul 27 2019

Keywords

35J25
35R30
49N60
49Q10
Polygonal inclusions
conductivity equation
shape derivative

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/00036811.2018.1469012

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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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author = "Elena Beretta and Elisa Francini and Sergio Vessella",

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AU - Francini, Elisa

AU - Vessella, Sergio

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N2 - 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.

AB - 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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KW - 49N60

KW - 49Q10

KW - Polygonal inclusions

KW - conductivity equation

KW - shape derivative

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

Abstract

Keywords

ASJC Scopus subject areas

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