Journal of Mathematical Sciences

, Volume 181, Issue 5, pp 632–667 | Cite as

Notes to the proof of a weighted Korn inequality for an elastic body with peak-shaped cusps

  • S. A. NazarovEmail author

We present the proof of the weighted anisotropic Korn inequality in a three-dimensional domain with peak-shaped cusps on the boundary. We verify the asymptotic accuracy of distribution of multipliers at the components of displacement vector and their derivatives in the corresponding weighted norm. We indicate conditions on a peak cusp under which the natural energy class is not embedded into a Sobolev or Lebesgue class. In the last case, the operator of elasticity problems possesses the continuous spectrum provoking wave processes in a finite volume (“black holes” for elastic waves). We also discuss possible generalizations of the result and open questions. Bibliography: 39 titles. Illustrations: 9 figures.


Black Hole Elastic Wave Elastic Body Elasticity Problem Hardy Inequality 
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© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Institute for Problems in Mechanical Engineering RASSt. PetersburgRussia

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