论文标题
Schauder估计锥体的产品
Schauder estimates on products of cones
论文作者
论文摘要
我们证明了对拉普拉斯（Laplacian）对具有欧几里得因素的二维锥的公制产品的内部估算，从而概括了唐纳森的工作并谴责了郭式的舒德尔估计。我们表征了锥体产物上均匀的亚次谐波功能的空间，并确定了在适当模型锥体的顶点的球中，可以很好地近似地测量球的尺度。然后，我们通过在这些量表下通过亚次级谐波函数在局部近似溶液，以测量第二个衍生物的Hölder连续性。
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.
