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Some Properties of Solutions to a Second Order Elliptic Equation with Principal Part of Divergence Form with Potential Concentrated on a Hypersurface

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Abstract

A number of classical results of the theory of second order elliptic equations of divergence form in ℝ d, d ⩾ 2, is generalized to problems with singular potential concentrated on a hypersurface of codimension 1. Such results are required, for example, for describing photon crystals. Bibliography: 8 titles.

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Authors
  1. S. V. Morozov
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Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 25–37.

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Morozov, S.V. Some Properties of Solutions to a Second Order Elliptic Equation with Principal Part of Divergence Form with Potential Concentrated on a Hypersurface. J Math Sci 132, 404–418 (2006). https://doi.org/10.1007/s10958-005-0507-2

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  • DOI: https://doi.org/10.1007/s10958-005-0507-2

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