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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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, 786–796 (2011). https://doi.org/10.1007/s10958-011-0436-1
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DOI: https://doi.org/10.1007/s10958-011-0436-1