Mapping properties of the heat operator on edge manifolds

Mathematics – Analysis of PDEs

Scientific paper

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30 pages, 2 figures

Scientific paper

We consider the heat operator on spaces with complete and incomplete edge
metrics. We establish its mapping properties, recovering and extending the
classical results from smooth manifolds and conical spaces. The estimates yield
short-time existence of solutions to certain semilinear parabolic equations.
Our discussion reviews and generalizes the earlier work by Jeffres and Loya.

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