Schauder estimates on products of cones

Martin de Borbon, Gregory Edwards

Research output: Contribution to specialist publicationArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages113-148
Number of pages36
Volume96
No.1
Specialist publicationCOMMENTARII MATHEMATICI HELVETICI
DOIs
Publication statusPublished - 12 Mar 2021

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