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Summary:
In the paper the solution of a thin plate reinforced with stiffening ribs is defined. A differential operator $\tilde{\Delta}^2$ (operator of a thin plate reinforced with thin-walled ribs) is introduced. For this operator properties of symmetry as well as of positive definiteness are proved on a linear subset $M\subset W^{(2)}_2(\Omega)$.
References:
[1] Г. H. Савіш H. П. Флеишмаи: Пластинки, оболочки с ребрами жесткости. Киев, 1964. Zbl 1230.62001
[2] С. Г. Михлин: Проблема минимума квадратичного функционала. Москва, 1952. Zbl 1145.11324
[3] С. Г. Михлин: Вариационные методы в математической физике. Москва, 1970. Zbl 1107.83313
[4] J. Nečas: Les méthods directes en théorie des équations elliptiques. Academia, Praha, 1967. MR 0227584
[5] S. L. Sobolev: Einige Anwendungen der Funktionalanalysis auf Gleichungen der mathematischen Physik. Akademia-Verlag, Berlin, 1964. MR 0172144
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