Hardy—Poincaré inequalities with boundary singularities

Mouhamed Moustapha Fall; Roberta Musina

doi:10.1017/S0308210510000740

Abstract

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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.

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