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Optimal coercivity inequalities in W1,p(Ω)

Published online by Cambridge University Press:  12 July 2007

Giles Auchmuty
Giles Auchmuty
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA ([email protected])
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Abstract

This paper describes the characterization of optimal constants for some coercivity inequalities in W1,p(Ω), 1 < p < ∞. A general result involving inequalities of p-homogeneous forms on a reflexive Banach space is first proved. The constants are shown to be the least eigenvalues of certain eigenproblems with equality holding for the corresponding eigenfunctions. This result is applied to three different classes of coercivity results on W1,p(Ω). The inequalities include very general versions of the Friedrichs and Poincaré inequalities. Scaling laws for the inequalities are also described.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 5 , October 2005 , pp. 915 - 933
Copyright
Copyright © Royal Society of Edinburgh 2005

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