Assume that $A=A(r,1)=\{x: r<||x||<1\} \subset R^n$ is an annulus.

Whether is known the constant of Poincaré inequality for A or some its estimation (w.r.t. $L^2$): the constant $C$ in the inequality $||f||_ {L^2(A)}\le C ||\nabla f||_{L^2(A)},$ where $ f\in W^{1,2}_0(A) $