Selfadjoint Extensions for the Elasticity System in Shape Optimization

Tom 52 / 2004

Serguei A. Nazarov, Jan Sokołowski Bulletin Polish Acad. Sci. Math. 52 (2004), 237-248 MSC: Primary 35B40, 35C20; Secondary 49Q10, 74P15. DOI: 10.4064/ba52-3-4


Two approaches are proposed to modelling of topological variations in elastic solids. The first approach is based on the theory of selfadjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and a variational formulation is established. For both approaches, accuracy estimates are derived.


  • Serguei A. NazarovInstitute of Mechanical Engineering Problems
    Laboratory of Mathematical Methods
    Russian Academy of Sciences
    V.O. Bol'shoi 61
    199178 St. Petersburg, Russia
  • Jan SokołowskiInstitut Elie Cartan
    Laboratoire de Mathématiques
    Université Henri Poincaré Nancy I
    B.P. 239
    54506 Vandœuvre-lès-Nancy Cedex, France

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