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  • Applied Mathematics  (1)
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    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 525-549 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We establish the best constants in the Poincaré-type and the trace-type inequalities for the quadratic form \documentclass{article}\pagestyle{empty}\begin{document}$ \lambda ||\,{\rm div}\,{\rm u}\,||_{L^2 }^2 \, + \,2\,\mu \,||\,\,(\nabla {\rm u}\, + \,\nabla {\rm u}^{\rm T})/2\,||_{L^2 }^2 $\end{document} which is fundamental in elasticity theory, on the space of H1 vector fields u on a slab vanishing on one or both of its sides. We similarly calculate those constants for the case of H1 divergence-free vector fields. Our method, which is fairly general, has another practical application to the quadratic form ∑j,k(ajk∂ku, ∂ju)L2 with coefficients a jk = akj ε C in H1 scalar functions u on a slab.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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