Geodesic
Selfadjoint Extensions for the Elasticity System in Shape Optimization
Serguei A. Nazarov1 ; Jan Sokołowski2
1Institute of Mechanical Engineering Problems Laboratory of Mathematical Methods Russian Academy of Sciences V.O. Bol'shoi 61 199178 St. Petersburg, Russia
2Institut Elie Cartan Laboratoire de Mathématiques Université Henri Poincaré Nancy I B.P. 239 54506 Vandœuvre-lès-Nancy Cedex, France
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 237-248
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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.
DOI : 10.4064/ba52-3-4
Keywords: approaches proposed modelling topological variations elastic solids first approach based theory selfadjoint extensions differential operators second approach function spaces separated asymptotics point asymptotic conditions introduced variational formulation established approaches accuracy estimates derived

Serguei A. Nazarov  1   ; Jan Sokołowski  2

1 Institute of Mechanical Engineering Problems Laboratory of Mathematical Methods Russian Academy of Sciences V.O. Bol'shoi 61 199178 St. Petersburg, Russia
2 Institut Elie Cartan Laboratoire de Mathématiques Université Henri Poincaré Nancy I B.P. 239 54506 Vandœuvre-lès-Nancy Cedex, France 
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Serguei A. Nazarov; Jan Sokołowski. Selfadjoint Extensions for the Elasticity System
 in Shape Optimization. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 237-248. doi: 10.4064/ba52-3-4

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