关于锥积的Schauder估计

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2020-02-18 DOI:10.4171/CMH/509

Martin de Borbon, Gregory Edwards

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引用次数: 3

摘要

我们用欧氏因子证明了拉普拉斯算子在二维锥的度量乘积上的一个内部Schauder估计，推广了Donaldson的工作，并重新提出了郭松的Schauder估值。我们在锥的乘积上刻画了齐次二次调和函数的空间，并确定了测地线球可以被以适当模型锥的顶点为中心的球很好地近似的尺度。然后，我们用次二次谐波函数在这些尺度上局部逼近解，以测量二阶导数的Holder连续性。

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Schauder estimates on products of cones

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 Holder continuity of second derivatives.

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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.