Open AccessHardy’s inequality for 𝑊^{1,𝑝}₀-functions on Riemannian manifolds
Author(s) -
V. M. Miklyukov,
Матти Вуоринен
Publication year - 1999
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-99-04849-2
Subject(s) - algorithm , artificial intelligence , type (biology) , computer science , mathematics , geology , paleontology
We prove that for every Riemannian manifold X \mathcal {X} with the isoperimetric profile of particular type there holds an inequality of Hardy type for functions of the class W 0 1 , p ( X ) W_0^{1,p}( \mathcal {X}) . We also study manifolds satisfying Hardy’s inequality and, in particular, we establish an estimate for the rate of growth of the weighted volume of the noncompact part of such a manifold.