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
URL:
http://dx.doi.org/10.1002/mma.1670170704
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