Spectral analysis for a discontinuous second order elliptic operator
Abstract
The spectrum of a second order elliptic operator S, with ellipticity constant α discontinuous in a point, is studied in L^p spaces. It turns out that, for (α, p) in a set A, classical results for the spectrum of smooth elliptic operators (see e.g. [3]) remain true for S; in particular, it is proved that S is the infinitesimal generator of an holomorphic semigroup . If (α, p) not in A, then the spectrum of S is the whole complex plane.
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