\(L^p\) resolvent estimates for constant coefficient elliptic systems on Lipschitz domains (Q457644)

Let \(L\) be an elliptic system of the second order with constant coefficients in \(\mathbb R^d\), and \(\partial /\partial \nu \) be the corresponding conormal derivative. It is studied the Neumann problem \(-Lu +\lambda u=f\) in \(\Omega \), \(\partial u/\partial \nu =0\) on \(\partial \Omega \), where \(\Omega \) is a bounded Lipschitz domain. It is shown that if \(u\in W^{1,2}(\Omega )\) is a solution of the problem then \([\int |u|^p]^{1/p} \leq C|\lambda |^{-1}[\int |f|^p]^{1/p}\).