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An optimization problem for the Biharmonic equation with Sobolev conditions

We state and solve an optimization problem about distribution of several supporting points under a Kirchhoff plate clamped along the boundary: the biharmonic equation is supplied with the Dirichlet boundary conditions and point Sobolev conditions. Some open questions are formulated. Bibliography: 23 titles.


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Correspondence to S. A. Nazarov.

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Dedicated to Vasilii Vasil’evich Zhikov

Translated from Problems in Mathematical Analysis 58, June 2011, pp. 69–77.

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Buttazzo, G., Nazarov, S.A. An optimization problem for the Biharmonic equation with Sobolev conditions. J Math Sci 176, 786 (2011).

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  • Optimal Location
  • Green Function
  • Dirichlet Problem
  • Elliptic Boundary
  • Biharmonic Equation