Calculus of Variations and Geometric Measure Theory
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V. Franceschi - D. Prandi - L. Rizzi

Recent results on the essential self-adjointness of sub-Laplacians, with some remarks on the presence of characteristic points

created by rizzi1 on 15 Mar 2019



Inserted: 15 mar 2019
Last Updated: 15 mar 2019

Journal: Séminaire de Théorie spectrale et géométrie (Grenoble)
Volume: 33
Pages: 1-15
Year: 2016
Doi: 10.5802/tsg.311


In this proceeding, we present some recent results obtained in 4 on the essential self-adjointness of sub-Laplacians on non-complete sub-Riemannian manifolds. A notable application is the proof of the essential self-adjointness of the Popp sub-Laplacian on the equiregular connected components of a sub-Riemannian manifold, when the singular region does not contain characteristic points. In their presence, the self-adjointness properties of (sub-)Laplacians are still unknown. We conclude the paper discussing the difficulties arising in this case.

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