This article is cited in 26 papers

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

E. M. Rudoy

M. A. Lavrent'ev Institute of Hydrodynamics

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.

Keywords: unilateral constraints, nonsmooth domain, cut, variational inequality, energy functional.

UDC: 517.946

Received: 13.10.2007
Revised: 18.03.2008

 English version: Siberian Mathematical Journal, 2009, 50:2, 341–354

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