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Gradient Estimates for the Perfect Conductivity Problem

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Abstract

We establish both upper and lower bounds of the gradient estimates for the perfect conductivity problem in the case where perfect (stiff) conductors are closely spaced inside an open bounded domain and away from the boundary. These results give the optimal blow-up rates of the stress for conductors with arbitrary shape and in all dimensions.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854, USA

    Ellen Shiting Bao, Yan Yan Li & Biao Yin

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Yan Yan Li

Authors
  1. Ellen Shiting Bao
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  2. Yan Yan Li
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  3. Biao Yin
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Correspondence to Yan Yan Li.

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Communicated by D. Kinderlehrer

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Bao, E.S., Li, Y.Y. & Yin, B. Gradient Estimates for the Perfect Conductivity Problem. Arch Rational Mech Anal 193, 195–226 (2009). https://doi.org/10.1007/s00205-008-0159-8

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  • DOI: https://doi.org/10.1007/s00205-008-0159-8

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