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Asymptotics of the energy functional for a fourth-order mixed boundary value problem in a domain with a cut. (Russian, English) Zbl 1224.35099

Sib. Mat. Zh. 50, No. 2, 429-444 (2009); translation in Sib. Math. J. 50, No. 2, 341-354 (2009).
Summary: 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.

MSC:

35J40 Boundary value problems for higher-order elliptic equations
35Q74 PDEs in connection with mechanics of deformable solids
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