亚椭圆PDE的正则性
Regularity for Subelliptic PDE Through Uniform Estimates in Multi-Scale Geometries
摘要：
我们的目的是审查和扩展一些最近的结果解决某些几何和解析估计的稳定性在黎曼近似subRiemann结构。特别地，我们将作者与Rea [19]和Manfredini [17]关于加倍性质的稳定性、Poincaré不等式、热核的Gaussian估计和Schauder估计的最近工作从Carnot群设置扩展到Hörmander向量场的一般情况。
英文摘要：
We aim at reviewing and extending a number of recent results addressing stability of certain geometric and analytic estimates in the Riemannian approximation of subRiemannian structures. In particular we extend the recent work of the the authors with Rea [19] and Manfredini [17] concerning stability of doubling properties, Poincaré inequalities, Gaussian estimates on heat kernels and Schauder estimates from the Carnot group setting to the general case of Hörmander vector fields.
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