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- W2016819005 abstract "When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the solution to the conductivity equation blows up in general. In this paper, we show that the solution to the conductivity equation can be decomposed into two parts in an explicit form: one of them has a bounded gradient and the gradient of the other part blows up. Using the decomposition, we derive the best possible estimates for the blow-up of the gradient. We then consider the case when the inclusions have positive permittivities. We show quantitatively that in this case the size of the blow-up is reduced." @default.
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- W2016819005 date "2009-12-01" @default.
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- W2016819005 title "Decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions" @default.
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- W2016819005 doi "https://doi.org/10.1016/j.jde.2009.08.005" @default.
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