Spectral theory of elliptic differential operators with indefinite weights

Details Spectral theory of elliptic differential operators with indefinite weights Spectral theory of elliptic differential operators with indefinite weights

2011-12-14

arxiv.org/abs/1112.3283v1

Mathematics

Spectral Theory

to appear in Proc. Roy. Soc. Edinburgh Sect. A

Scientific paper

The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal spectrum of the associated elliptic operator in $L^2(\Omega)$ is bounded. In the special case that $\Omega=R^n $decomposes into subdomains $\Omega_+$ and $\Omega_-$ with smooth compact boundaries and the weight function is positive on $\Omega_+$ and negative on $\Omega_-$, it turns out that the nonreal spectrum consists only of normal eigenvalues which can be characterized with a Dirichlet-to-Neumann map.

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