Elliptic Eigenvalue Problems Involving an~Indefinite Weight Function

S. G. Pyatkov

Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 138-154

Résumé

We study elliptic eigenvalue problems with indefinite weight function; i.e., the problems $Lu=\lambda g(x)u$ ($x\in G\subset\mathbb R^n$) and $B_ju\big|_{\Gamma}=0$ ($j=\overline{1,m}$), where $L$ is a selfadjoint (in $L_2(G)$) elliptic operator, $g(x)$ is a measurable function changing sign in $G$, and $\{B_j\}$ is a collection of boundary operators. Under consideration is the question on the unconditional basis property of eigenfunctions and associated functions of this problem in the space $L_2$ with weight $|g|$.