Geodesic
Existence criteria in some extremum problems involving eigenvalues of elliptic operators
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 37-47

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Some existence criteria for a certrain class of extremum problems involving eigenvalues of linear elliptic boundary-value problems (including ones in the form of variational inequalities) are proved. The approach applied admits an extension to the case of extremum problems associated with eigenvalues of nonlinear boundary-value problems. Some applications to optimal structural design and comparisons with results in the literature are given.
Keywords: eigenvalue optimization problem, elliptic boundary-value problem, variational inequality, existence theorem, optimal structural design. 
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     author = {Vasily Yu. Goncharov},
     title = {Existence criteria in some extremum problems involving eigenvalues of elliptic operators},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {37--47},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a4/}
}
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Vasily Yu. Goncharov. Existence criteria in some extremum problems involving eigenvalues of elliptic operators. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 37-47. http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a4/