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Gradient estimates for solutions to the conductivity problem

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Abstract.

In this paper we derive very precise gradient estimates for solutions to the conductivity problem in the case where two circular conductivity inclusions are very close but not touching. The novelty of these estimates is that they give very specific information about the blow up of the gradient as the conductivities of the inclusions degenerate.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Habib Ammari & Mikyoung Lim

  2. School of Mathematical Sciences, Seoul National University, Seoul, 151-747, Korea

    Hyeonbae Kang

Authors
  1. Habib Ammari
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  2. Hyeonbae Kang
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  3. Mikyoung Lim
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Mathematics Subject Classification (2000): 35J25, 73C40

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Ammari, H., Kang, H. & Lim, M. Gradient estimates for solutions to the conductivity problem. Math. Ann. 332, 277–286 (2005). https://doi.org/10.1007/s00208-004-0626-y

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  • DOI: https://doi.org/10.1007/s00208-004-0626-y

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