Optimal coercivity inequalities in W 1, p (Ω)

This paper describes the characterization of optimal constants for some coercivity inequalities in W 1, 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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2005-10, Vol.135 (5), p.915-933
1. Verfasser: Auchmuty, Giles
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:This paper describes the characterization of optimal constants for some coercivity inequalities in W 1, 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 W 1, p (Ω). The inequalities include very general versions of the Friedrichs and Poincaré inequalities. Scaling laws for the inequalities are also described.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210500004182