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Asymptotics of the energy functional for a fourth-order mixed boundary value problem in a domain with a cut

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Abstract

We study a fourth-order elliptic equation in a domain with a curvilinear cut. There are unilateral constraints for the solution on the cut. Considering rather general sufficiently smooth perturbations of the domain, we study the asymptotics of the energy functional. We deduce a formula for the derivative of the energy functional with respect to the perturbation parameter of the domain.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Novosibirsk, Russia

    E. M. Rudoy

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Correspondence to E. M. Rudoy.

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Original Russian Text Copyright © 2009 Rudoy E. M.

The author was supported by the Russian Foundation for Basic Research (Grant 06-01-00209) and the President of the Russian Federation (Grant MK-4338.2008.1).

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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 430–445, March–April, 2009.

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Rudoy, E.M. Asymptotics of the energy functional for a fourth-order mixed boundary value problem in a domain with a cut. Sib Math J 50, 341–354 (2009). https://doi.org/10.1007/s11202-009-0039-y

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  • DOI: https://doi.org/10.1007/s11202-009-0039-y

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