Glushak, A. V.; Transirico, M.; Troisi, M. Embedding theorems for elliptic equations in unbounded domains. (Italian. English summary) Zbl 0763.35028 Rend. Mat. Appl., VII. Ser. 9, No. 1, 113-130 (1989). Let \(\rho(x)=(1+| x|)/2\) defined on a smooth unbounded open set \(\Omega\) with bounded boundary. The authors study some weighted Sobolev spaces among which is \(W^ m_{\sigma}(\Omega)\) defined using the weight \(\rho^{2\sigma}\). As an application, the estimate \(| u|_{W^ 2_{\sigma}(\Omega)}\leq k (| Lu|_{L^ 2_{\sigma}(\Omega)}+| u|_{2,\Omega_ o})\) is obtained, where \(Lu\) is an elliptic linear differential operator satisfying the Cordes condition and \(\Omega_ o\) is a bounded open subset of \(\Omega\). Reviewer: J.J.Manfredi (Pittsburgh) Cited in 5 Documents MSC: 35J25 Boundary value problems for second-order elliptic equations 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:weighted Sobolev spaces; elliptic linear differential operator; Cordes condition PDFBibTeX XMLCite \textit{A. V. Glushak} et al., Rend. Mat. Appl., VII. Ser. 9, No. 1, 113--130 (1989; Zbl 0763.35028)