Abstract
Given a manifoldB with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale ofL p -Sobolev spaces. Ellipticity is proven to be equivalent to the Fredholm property in these spaces; it turns out to be independent of the choice ofp. We then show that the cone algebra is closed under inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to analyze the behaviour of these operators onL p (B).
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Schrohe, E., Seiler, J. Ellipticity and invertibility in the cone algebra onL p -Sobolev spaces. Integr equ oper theory 41, 93–114 (2001). https://doi.org/10.1007/BF01202533
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DOI: https://doi.org/10.1007/BF01202533