Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Complex powers for cone differential operators and the heat equation on manifolds with conical singularities


Author: Nikolaos Roidos
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
Published electronically: February 16, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35K05, 35K65, 35R01, 46B70, 58J35

Retrieve articles in all journals with MSC (2010): 35K05, 35K65, 35R01, 46B70, 58J35


Additional Information

Nikolaos Roidos
Affiliation: Institut für Analysis, Leibniz Universität, Hannover, Germany 30167
Email: roidos@math.uni-hannover.de

DOI: https://doi.org/10.1090/proc/13986
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
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society