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Schauder estimates on products of cones

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journal contribution
posted on 2023-11-09, 14:43 authored by Martin de BorbonMartin de Borbon, Gregory Edwards
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.

Funding

Curvature constraints and space of metrics – CCEM

Agence Nationale de la Recherche

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National Science Foundation RTG: Geometry and Topology at the University of Notre Dame, grant number DMS1547292

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Commentarii Mathematici Helvetici

Volume

96

Issue

1

Pages

113 - 148

Publisher

EMS Press

Version

  • AM (Accepted Manuscript)

Rights holder

© EMS Press

Publisher statement

This paper was accepted for publication in the journal Commentarii Mathematici Helvetici and the definitive published version is available at https://doi.org/10.4171/CMH/509

Publication date

2021-03-13

Copyright date

2021

ISSN

0010-2571

eISSN

1420-8946

Language

  • en

Depositor

Dr Martin De Borbon. Deposit date: 8 November 2023

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