On Persson's theorem in local Dirichlet spaces
The author considers a strongly, local, regular and irreducible Dirichlet form \(\epsilon.\) He studies the analogue of the theorem of \textit{A. Persson} that is proved in [Math. Scand. 8, 143-153 (1960; Zbl 0145.14901)]to obtain a version, in his context, of his variational characterization of the bottom of the essential spectrum of elliptic differential operators in divergence form. Then, the author uses his result and those in cooperation with \textit{F. Cipriani} [J. Reine Angew. Math. 496, 163-179 (1998; Zbl 0891.35016)] to prove suitable coercitivity conditions and weighted \(L^p\) bounds for those eigenfunctions of the self-adjoint operator associated to \(\varepsilon\) whose eigenvalue lies below the essential spectrum of the ``small eigenfunctions''. To obtain this result the author uses a process contained in the book of \textit{S. A. Agmon} [Lectures on exponential decay of solutions of second-order elliptic equations, Princeton Univ. Press (1982; Zbl 0503.35001)].
elliptic differential operators in divergence form
scientific article; zbMATH DE number 1182351