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Elliptic operators of variational form in unbounded domains in \(R^ n\). (Italian. English summary) Zbl 0678.35018

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
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