Linear elliptic equations in composite media with anisotropic fibres

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Yeh, Li-Ming¹ 

[1] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 30050, Taiwan

关键词: Money space;    Campanato space;    Anisotropic fibres;    Longitudinal direction;    Transverse direction;   

DOI  :  10.1016/j.jde.2018.11.036

来源: Elsevier

【 摘 要 】

Linear elliptic equations in composite media with anisotropic fibres are concerned. The media consist of a periodic set of anisotropic fibres with low conductivity, included in a connected matrix with high conductivity. Inside the anisotropic fibres, the conductivity in the longitudinal direction is relatively high compared with that in the transverse directions. The coefficients of the elliptic equations depend on the conductivity. This work is to derive the Holder and the gradient L-P estimates (uniformly in the period size of the set of anisotropic fibres as well as in the conductivity ratio of the fibres in the transverse directions to the connected matrix) for the solutions of the elliptic equations. Furthermore, it is shown that, inside the fibres, the solutions have higher regularity along the fibres than in the transverse directions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free