Removable sets for homogeneous linear partial differential equations in Carnot groups

Let L be a homogeneous left-invariant differential operator on a Carnot group. Assume that both L and L t are hypoelliptic. We study the removable sets for L -solutions. We give precise conditions in terms of the Carnot- Caratheodory Hausdorff dimension for the removability for L -solutions under se...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2016-02, Vol.128 (1), p.215-238
Main Authors: Chousionis, Vasilis, Tyson, Jeremy T.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Criteria
Dynamical Systems and Ergodic Theory
Functional Analysis
Ingredients
Integral calculus
Mathematics
Mathematics and Statistics
Operators
Partial Differential Equations
Regularity
Self-similarity
Tiling
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Summary:Let L be a homogeneous left-invariant differential operator on a Carnot group. Assume that both L and L t are hypoelliptic. We study the removable sets for L -solutions. We give precise conditions in terms of the Carnot- Caratheodory Hausdorff dimension for the removability for L -solutions under several auxiliary integrability or regularity hypotheses. In some cases, our criteria are sharp on the level of the relevant Hausdorff measure. One of the main ingredients in our proof is the use of novel local self-similar tilings in Carnot groups.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-016-0007-y