Regularity for subelliptic PDE through uniform estimates in multi-scale geometries

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 (Math Ann 357(3):1175–1198, 2013 ) and Manfre...

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Bibliographic Details
Published in:Bulletin of mathematical sciences 2016-07, Vol.6 (2), p.173-230
Main Authors: Capogna, Luca, Citti, Giovanna
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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 (Math Ann 357(3):1175–1198, 2013 ) and Manfredini (Anal Geom Metric Spaces 1:255–275, 2013 ) concerning stability of doubling properties, Poincare’ inequalities, Gaussian estimates on heat kernels and Schauder estimates from the Carnot group setting to the general case of Hörmander vector fields.
ISSN:1664-3607
1664-3615
DOI:10.1007/s13373-015-0076-8