TY - JOUR
T1 - Asymptotics for the concentrated field between closely located hard inclusions in all dimensions
AU - Zhao, Zhiwen
AU - Hao, Xia
N1 - Funding Information:
The AACES study was funded by NCI ( CA142081-01A1 ). Additional support was provided by Metropolitan Detroit Cancer Surveillance System (MDCSS) with federal funds from the National Cancer Institute , National Institute of Health , Dept. of Health and Human Services , under Contract No. HHSN261201000028C and the Epidemiology Research Core , supported in part by NCI Center Grant ( P30CA22453 ) to the Karmanos Cancer Institute, Wayne State University School of Medicine.
Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.
PY - 2021/6
Y1 - 2021/6
N2 - When hard inclusions are frequently spaced very closely, the elec- tric field, which is the gradient of the solution to the perfect conductivity equation, may be arbitrarily large as the distance between two inclusions goes to zero. In this paper, our objectives are two-fold: First, we extend the as- ymptotic expansions of [26] to the higher dimensions greater than three by capturing the blow-up factors in all dimensions, which consist of some certain integrals of the solutions to the case when two inclusions are touching; second, our results answer the optimality of the blow-up rate for any m; n ≥ 2, where m and n are the parameters of convexity and dimension, respectively, which is only partially solved in [29].
AB - When hard inclusions are frequently spaced very closely, the elec- tric field, which is the gradient of the solution to the perfect conductivity equation, may be arbitrarily large as the distance between two inclusions goes to zero. In this paper, our objectives are two-fold: First, we extend the as- ymptotic expansions of [26] to the higher dimensions greater than three by capturing the blow-up factors in all dimensions, which consist of some certain integrals of the solutions to the case when two inclusions are touching; second, our results answer the optimality of the blow-up rate for any m; n ≥ 2, where m and n are the parameters of convexity and dimension, respectively, which is only partially solved in [29].
KW - Asymptotic expansions
KW - M-convex in- clusions
KW - Optimal blow-up rate
KW - Perfect conductivity problem
UR - https://www.scopus.com/pages/publications/85107588219
U2 - 10.3934/cpaa.2021086
DO - 10.3934/cpaa.2021086
M3 - Article
AN - SCOPUS:85107588219
SN - 1534-0392
VL - 20
SP - 2379
EP - 2398
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 6
ER -