Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610357 | Journal of Differential Equations | 2014 | 22 Pages |
Abstract
In the study of composites, it is important to determine the shape of inclusions. There is an interesting case in conductivity problem that the inclusion is insulated. In present paper, we first obtain the representation formula of the solution to an exterior problem, and then prove that for any uniform loading such solution can be extended into the inclusion as an affine function if and only if the insulated inclusion is an ellipse or an ellipsoid. We also show that an analogous result holds for the elasticity problem, which is related to Eshelby conjecture. The main results in this paper are motivated by Ammari, Kang, Kim and Lee (2013), Ammari, Kang and Lim (2005), Kang and Milton (2008), and Liu (2008).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Bo Wang, Haigang Li, Jiguang Bao,