Hardy-Poincaré inequalities with boundary singularities

Fall, Mouhamed Moustapha;Musina, Roberta
(2012) Proceedings / The Royal Society of Edinburgh. Section A, Mathematics — Vol. 142, n° 4, p. 769-786 (2012)

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  • Fall, Mouhamed Moustapha
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  • Musina, Roberta
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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 H <inf>0</inf> <sup>1</sup>(Ω), where Ω is a bounded domain in ℝ <sup>N</sup>, N ≥ 2, with 0 ∈ ∂ Ω. In particular, we give sufficient and necessary conditions so that the best constant is achieved. © Copyright 2012 Royal Society of Edinburgh.

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Fall, M. M., & Musina, R. (2012). Hardy-Poincaré inequalities with boundary singularities. Proceedings / The Royal Society of Edinburgh. Section A, Mathematics, 142(4), 769-786. https://doi.org/10.1017/S0308210510000740 (Original work published 2012)