Second-Order Elliptic Equation of Divergence Form Having a Compactly Supported Solution

Abstract

An equation of the form -div (g∇u) = λu has a solution u of class C 0 ∞ , where g is a real positive definite matrix-valued function belonging to the Holder classes with exponent less than 1. From the spectral point of view, this means that there exists a Schrodinger operator with periodic metric and the spectrum of this operator contains an eigenvalue of infinite multiplicity. Bibliography: 9 titles.