Poincare inequality?

Let Ω be a smooth bounded open subset of Rn. Does there exist A=A(Ω) with the property that for any fC(ˉΩ) with f=0 on Ω, Ω|f(x)|dxAΩ|f(x)|dx? I think that this is known as some version of “Poincare’s inequality”.

Answer

I found the answer at http://anhngq.wordpress.com/2010/02/22/the-poincare-inequality/. By Holder’s Inequality and Poincare’s Inequality for W1,p0 spaces, there exist A(Ω),B(Ω)>0 such that

Attribution
Source : Link , Question Author : Stefan Smith , Answer Author : Stefan Smith

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