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Volume 37, Issue 1
Singular Functions and Characterizations of Field Concentrations: A Survey

Hyeonbae Kang & Sanghyeon Yu

DOI: 10.4208/ata.2021.pr80.08

Anal. Theory Appl., 37 (2021), pp. 102-113.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics (Laplace equation), linear elasticity (Lamé system), and viscous flow (Stokes system). This paper is to review such progress in a coherent way.

  • Keywords

Field concentration, gradient blow-up, closely spaced inclusions, extreme inclusions, Laplace equation, Lamé system, Stokes system.

  • AMS Subject Headings

35J47, 35B40, 35B45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-37-102, author = {Kang , Hyeonbae and Yu , Sanghyeon}, title = {Singular Functions and Characterizations of Field Concentrations: A Survey}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {37}, number = {1}, pages = {102--113}, abstract = {

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics (Laplace equation), linear elasticity (Lamé system), and viscous flow (Stokes system). This paper is to review such progress in a coherent way.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2021.pr80.08}, url = {http://global-sci.org/intro/article_detail/ata/18766.html} }
TY - JOUR T1 - Singular Functions and Characterizations of Field Concentrations: A Survey AU - Kang , Hyeonbae AU - Yu , Sanghyeon JO - Analysis in Theory and Applications VL - 1 SP - 102 EP - 113 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/ata.2021.pr80.08 UR - https://global-sci.org/intro/article_detail/ata/18766.html KW - Field concentration, gradient blow-up, closely spaced inclusions, extreme inclusions, Laplace equation, Lamé system, Stokes system. AB -

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics (Laplace equation), linear elasticity (Lamé system), and viscous flow (Stokes system). This paper is to review such progress in a coherent way.

Kang , Hyeonbae and Yu , Sanghyeon. (2021). Singular Functions and Characterizations of Field Concentrations: A Survey. Analysis in Theory and Applications. 37 (1). 102-113. doi:10.4208/ata.2021.pr80.08
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