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Hardy—Poincaré inequalities with boundary singularities

Published online by Cambridge University Press:  10 August 2012

Mouhamed Moustapha Fall  and
Roberta Musina
Mouhamed Moustapha Fall
Affiliation:
Département de Mathématique, Université Catholique de Louvain-La-Neuve, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium (mouhamed.fall@uclouvain.be)
Roberta Musina
Affiliation:
Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 206, 33100 Udine, Italy (musina@dimi.uniud.it)
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Abstract

We are interested in variational problems involving weights that are singular at a point of the boundary of the domain. More precisely, we study a linear variational problem related to the Poincaré inequality and to the Hardy inequality for maps in H01(Ω), where Ω is a bounded domain in ℝN, N ≥ 2, with 0 ∈ ∂Ω. In particular, we give sufficient and necessary conditions so that the best constant is achieved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 4 , August 2012 , pp. 769 - 786
Copyright
Copyright © Royal Society of Edinburgh 2012

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