An eigenvalue problem related to Hardy’s $L^P$ inequality

Moshe Marcus; Itai Shafrir

Displaying similar documents to “An eigenvalue problem related to Hardy’s $L^{P}$ inequality”

Hardy's inequalities revisited

Haïm Brezis, Moshe Marcus (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

Xiaming Chen, Renjin Jiang, Dachun Yang (2016)

Analysis and Geometry in Metric Spaces

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Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with...

A certain modification of Hardy's inequality

B. Florkiewicz, A. Rybarski (1972)

Colloquium Mathematicae

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Hardy-type inequalities related to degenerate elliptic differential operators

Lorenzo D’Ambrosio (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators $L_{p} u : = - \nabla_{L}^{*} ({|\nabla_{L} u|}^{p - 2} \nabla_{L} u)$ . If $φ$ is a positive weight such that $- L_{p} φ \geq 0$ , then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.