Schauder estimates on products of cones
| Autor: | Martin de Borbon, Gregory Edwards |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Geodesic General Mathematics 010102 general mathematics Mathematical analysis Hölder condition 01 natural sciences Measure (mathematics) Mathematics - Analysis of PDEs Differential Geometry (math.DG) Cone (topology) Harmonic function Metric (mathematics) FOS: Mathematics Schauder estimates 0101 mathematics Laplace operator Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Commentarii Mathematici Helvetici. 96:113-148 |
| ISSN: | 0010-2571 |
| DOI: | 10.4171/cmh/509 |
| Popis: | 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 H\"older continuity of second derivatives. Comment: 27 pages, 2 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|