Sobolev spaces on multiple cones
Classical Analysis and ODEs
2010-05-31 v4 Functional Analysis
Metric Geometry
Abstract
The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from . The analysis interestingly combines use of Poincar\'e inequalities and of some Hardy type inequalities.
Cite
@article{arxiv.0812.1146,
title = {Sobolev spaces on multiple cones},
author = {Pascal Auscher and Nadine Badr},
journal= {arXiv preprint arXiv:0812.1146},
year = {2010}
}
Comments
Modifications following the referee's suggestions. Some typos and math typos corrected. Addition of references to Poincar\'e inequalities on spheres