Hardy—Poincaré inequalities with boundary singularities

By M. Fall, R. Musina. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2010

48 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0f9cd9f393d6afff54fdbbdffab6e67e02733b15

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In Applied Mathematics

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Citations in the corpus

• OPTIMAL HARDY WEIGHT FOR SECOND-ORDER ELLIPTIC OPERATOR: AN ANSWER TO A PROBLEM OF AGMON (2012, background): “lows from Theorem 11.6 that Wis an optimal Hardy-weight, and that the spectrum and the essential spectrum of W−1(−∆) is [1,∞). Note that (11.1) and the global optimality of the constant is known (cf. [21, 36]). Throughout this section (unless otherwise stated), we assume that the Martin boundary δΩ ”