Troisi, Mario Elliptic operators of variational form in unbounded domains in \(R^ n\). (Italian. English summary) Zbl 0678.35018 Ric. Mat. 36, Suppl., 35-51 (1987). The author studies the coercivity of certain sesquilinear forms of the type \[ b(u,v):=\int_{\Omega}\sum_{| p|,| q| \leq m}b_{pq}(x)D^ pu(x)\overline{D^ qv(x)} dx \] where the domain \(\Omega \subset {\mathbb{R}}^ n\) is unbounded and the functions u, v are elements of suitable weighted Sobolev spaces. Among other things various inequalities of Gårding type are established. Reviewer: M.Fuchs MSC: 35J35 Variational methods for higher-order elliptic equations 35B45 A priori estimates in context of PDEs 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:Dirichlet problems; unbounded domains; coercivity; sesquilinear forms; weighted Sobolev spaces; inequalities of Gårding type PDFBibTeX XMLCite \textit{M. Troisi}, Ric. Mat. 36, 35--51 (1987; Zbl 0678.35018)