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Well‐Posedness of Mixed Formulations in Elasticity
Author(s) -
Romano G.,
Rosati L.,
Diaco M.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199907)79:7<435::aid-zamm435>3.0.co;2-f
Subject(s) - elasticity (physics) , linear elasticity , uniqueness , mathematics , linear subspace , mathematical analysis , hilbert space , pure mathematics , finite element method , physics , thermodynamics
Mixed formulations in elasticity are analysed and existence and uniqueness of the solution are discussed in the context of Hilbert space theory. New results, referred to in the analysis of elasticity problems, are proved. They are concerned with the closedness of the product of two linear operators and a projection property equivalent to the closedness of the sum of two closed subspaces. A set of two necessary and sufficient conditions for the well‐posedness of an elastic problem with a singular elastic compliance provides the most general result of this kind in linear elasticity. Sufficient criteria for the well‐posedness of elastic problems in structural mechanics including the presence of supporting elastic beds are contributed and applications are exemplified.