Spectral analysis for a discontinuous second order elliptic operator
Paolo Manselli, Francesco Ragnedda · DOAJ (DOAJ: Directory of Open Access Journals) · 2003
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.