×

On essential self-adjointnee of semi-bounded elliptic second order operators without requirement of completeness of the Riemannian manifold. (Russian. English summary) Zbl 0844.35024

Summary: Conditions are obtained for the general type symmetric elliptic second-order operator \(L\) in the space \(L_2(G)\) (\(D_L= C^2_0(G)\), \(G\) is an open set in \(\mathbb{R}^n\)) at which semi-boundedness involves its essential selfadjointness without assumption of completeness of \(G\) in the Riemannian manifold metric, which is specified by the matrix \(A^{- 1}(x)\), where \(A(x)\) is a matrix of higher-order coefficients of the operator \(L\).

MSC:

35J15 Second-order elliptic equations
47F05 General theory of partial differential operators
58J05 Elliptic equations on manifolds, general theory
PDFBibTeX XMLCite