Complex powers for cone differential operators and the heat equation on manifolds with conical singularities
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Abstract:
We obtain left and right continuous embeddings for the domains of the complex powers of sectorial $\mathbb {B}$-elliptic cone differential operators. We apply this result to the heat equation on manifolds with conical singularities and provide asymptotic expansions of the unique solution close to the conical points. We further show that the decomposition of the solution in terms of asymptotics spaces, i.e., finite-dimensional spaces that describe the domains of the integer powers of the Laplacian and determined by the local geometry around the singularity, is preserved under the evolution.References
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Additional Information
- Nikolaos Roidos
- Affiliation: Institut für Analysis, Leibniz Universität, Hannover, Germany 30167
- MR Author ID: 1016149
- Email: roidos@math.uni-hannover.de
- Received by editor(s): February 7, 2017
- Received by editor(s) in revised form: September 30, 2017
- Published electronically: February 16, 2018
- Communicated by: Joachim Krieger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2995-3007
- MSC (2010): Primary 35K05, 35K65, 35R01, 46B70, 58J35
- DOI: https://doi.org/10.1090/proc/13986
- MathSciNet review: 3787360