The Fredholm index of a second order elliptic system on an infinite cylinder

This paper investigates the Fredholmness of a second order elliptic system on an infinite cylinder in various weighted or non-weighted Sobolev spaces, assuming homogeneous Dirichlet boundary conditions and suitable asymptotic behavior of the coefficients. It is shown that the index coincides with the spectral flow of an associated parametrized family of elliptic systems on the cross-section of the cylinder. Dependence or independence of the index upon the functional setting is discussed along with their impact on spectral invariance and elliptic regularity.