A transmission problem on a polygonal partition: regularity and shape differentiability. Issue 10 (27th July 2019)

• Record Type: Journal Article
• Authors: Beretta, Elena; Francini, Elisa; Vessella, Sergio
• Is Part Of: Applicable analysis. Volume 98:Issue 10(2019)
• Page Start: 1862
• Page End: 1874
• Publication Date: 2019-07-27
• Subjects: Polygonal inclusions -- conductivity equation -- shape derivative; 35R30 -- 35J25 -- 49Q10 -- 49N60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1469012
• Languages: English
• ISSNs: 0003-6811

Abstract

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.