Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés. (Remarks on linear second order elliptic equations in divergence form on unbounded domains). (French) Zbl 0656.35030

Lions, Pierre Louis

Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 79, 178-183 (1985).

We prove the existence and uniqueness of the solution of the problem \(Au=f\), \(u\in H^ 1_ 0(\Omega)\) in the case that \(\Omega\) is an open unbounded domain in \({\mathbb{R}}^ n\), A is a second order elliptic variational operator with bounded and measurable coefficients and f belongs to \(H^{-1}(\Omega)\).

MSC:

35J25	Boundary value problems for second-order elliptic equations
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35R05	PDEs with low regular coefficients and/or low regular data

Keywords:

existence; uniqueness; unbounded domain; variational operator; measurable coefficients