an:03849687
Zbl 0535.35018
Nguyen Xuan Dung
Essential self-adjointness and self-adjointness for even order elliptic operators
EN
Proc. R. Soc. Edinb., Sect. A 93, 161-179 (1982).
00224139
1982
j
35J30 47B25 35P05 35P25
essential self-adjointness; self-adjointness; even order elliptic operators
The subject of this paper are symmetric elliptic operators on \(L^ 2({\mathbb{R}}^ n)\), of the form \(T=\sum_{0<| \alpha |,| \beta | \leq m}(-1)^{| \alpha |}D^{\alpha}a_{\alpha \beta}(x)D^{\beta}+q(x).\) For the first it is proved that T is essentially self adjoint on \(C_ 0\!^{\infty}({\mathbb{R}}^ n)\) if the \(a_{\alpha \beta}\) are sufficiently smooth and bounded and \(q(x)\geq - cons\tan t\quad | x|^{2m/(2m-1)}.\) Then it is proved that such an operator is self-adjoint on \(H^{2m}({\mathbb{R}}^ n)\cap D(q)\) if q is positive and \(| D^{\alpha}q| \leq \quad cons\tan t\quad q^{1+| \alpha | /2m},\) for \(1<| \alpha | \leq m\). This extends earlier results which had more restrictions on the operator.
G.Gudmundsdottir