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Schauder estimates on products of cones

Research output: Contribution to specialist publicationArticle

Martin de Borbon, Gregory Edwards

Original languageEnglish
Number of pages36
Issue number1
E-pub ahead of print12 Mar 2021
Published12 Mar 2021

Bibliographical note

Publisher Copyright: © 2021 Swiss Mathematical Society

King's Authors


We prove an interior Schauder estimate for the Laplacian on metric products of two dimensional cones with a Euclidean factor, generalizing the work of Donaldson and reproving the Schauder estimate of Guo–Song. We characterize the space of homogeneous subquadratic harmonic functions on products of cones, and identify scales at which geodesic balls can be well approximated by balls centered at the apex of an appropriate model cone. We then locally approximate solutions by subquadratic harmonic functions at these scales to measure the Hölder continuity of second derivatives.

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