Rudoy, E. M. 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. Cited in 13 Documents MSC: 35J40 Boundary value problems for higher-order elliptic equations 35Q74 PDEs in connection with mechanics of deformable solids Keywords:unilateral constraints; nonsmooth domain; cut; variational inequality; energy functional PDFBibTeX XMLCite \textit{E. M. Rudoy}, Sib. Mat. Zh. 50, No. 2, 429--444 (2009; Zbl 1224.35099); translation in Sib. Math. J. 50, No. 2, 341--354 (2009) Full Text: EuDML EMIS