Poincaré Inequality on Subanalytic Sets
Keyword(s):
AbstractLet $$\Omega $$ Ω be a subanalytic connected bounded open subset of $$\mathbb {R}^n$$ R n , with possibly singular boundary. We show that given $$p\in [1,\infty )$$ p ∈ [ 1 , ∞ ) , there is a constant C such that for any $$u\in W^{1,p}(\Omega )$$ u ∈ W 1 , p ( Ω ) we have $$||u-u_{\Omega }||_{L^p} \le C||\nabla u||_{L^p},$$ | | u - u Ω | | L p ≤ C | | ∇ u | | L p , where we have set $$u_{\Omega }:=\frac{1}{|\Omega |}\int _{\Omega } u.$$ u Ω : = 1 | Ω | ∫ Ω u .
Keyword(s):
2012 ◽
Vol 14
(03)
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pp. 1250023
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2014 ◽
Vol 2015
(17)
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pp. 8116-8151
2014 ◽
Vol 35
(4)
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pp. 575-598
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2008 ◽
Vol 51
(2)
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pp. 529-543
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2015 ◽
Vol 59
(2)
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pp. 261-280
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