A transmission problem on a polygonal partition: regularity and shape differentiability
Analysis of PDEs
2020-12-29 v1
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.
Cite
@article{arxiv.1801.09396,
title = {A transmission problem on a polygonal partition: regularity and shape differentiability},
author = {Elena Beretta and Elisa Francini and Sergio Vessella},
journal= {arXiv preprint arXiv:1801.09396},
year = {2020}
}