Regularity for Subelliptic Pde Through Uniform Estimates in Multi-scale Geometries

Authors

Luca Capogna, Worcester Polytechnic InstituteFollow
Giovanna Citti, Alma Mater Studiorum Università di Bologna

Document Type

Article

Publication Date

7-1-2016

Publication Title

Bulletin of Mathematical Sciences

Abstract

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.

Keywords

Heat kernels, Riemannian approximation, Subelliptic PDE, SubRiemannian geometry

Volume

6

Issue

2

First Page

173

Last Page

230

DOI

10.1007/s13373-015-0076-8

ISSN

16643607

Comments

Archived as published.

Recommended Citation

Capogna, Luca and Citti, Giovanna, "Regularity for Subelliptic Pde Through Uniform Estimates in Multi-scale Geometries" (2016). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/129