Mapping Properties of the Heat Operator on Edge Manifolds
Publication Date
2015
Description
We consider the heat operator acting on differential forms on spaces with complete and incomplete edge metrics. In the latter case we study the heat operator of the Hodge Laplacian with algebraic boundary conditions at the edge singularity. We establish the mapping properties of the heat operator, recovering and extending the classical results from smooth manifolds and conical spaces. The estimates, together with strong continuity of the heat operator, yield short-time existence of solutions to certain semilinear parabolic equations. Our discussion reviews and generalizes earlier work by Jeffres and Loya.
Journal
Mathematische Nachrichten
Volume
288
Department
Mathematics
Link to Published Version
http://onlinelibrary.wiley.com/doi/10.1002/mana.201300188/abstract
DOI
10.1002/mana.201300188
Recommended Citation
Bahuaud, Eric; Dryden, Emily; and Vertman, Boris. "Mapping Properties of the Heat Operator on Edge Manifolds." Mathematische Nachrichten (2015) .