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Local compactness for linear elasticity in irregular domains
Author(s) -
Weck Norbert
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170204
Subject(s) - mathematics , embedding , compact space , elasticity (physics) , pure mathematics , mathematical analysis , integrable system , square integrable function , boundary value problem , linear elasticity , property (philosophy) , finite element method , philosophy , materials science , physics , epistemology , artificial intelligence , computer science , composite material , thermodynamics
Abstract For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector‐valued L 2 ‐functions whose symmetrized Jacobians are square‐integrable should be compactly embedded in L 2 . For regions with the cone property this is usually achieved by combining Korn's inequalities and Rellich's selection theorem. We shall show that in a class of less regular regions Korn's second inequality fails whereas the desired compact embedding still holds true.