Consider theorem (0x68a308c3) . How the constants \(C_1\), \(C_2\) and \(\tau\) look like for \(\Omega=(-Q,Q)^d\), \(\Sigma=\partial B_1\) and \(A=\chi_{\Omega_+} a_+ + \chi_{\Omega_-}a_-\), where \(Q>1\), \(\Omega_+=B_1\) and \(\Omega_-=\Omega\setminus \overline{B_1}\)?
Note, we set \(D=\{x\in \Omega\mid \dist (x,\partial \Omega)>h\}\). Obviously, this is the maximal allowed \(D\) and the inequality is true for all other \(D'\) with the same constant.