Calculus of Variations and Geometric Measure Theory

V. Franceschi - D. Prandi - L. Rizzi

On the essential self-adjointness of singular sub-Laplacians

created by franceschi on 31 Aug 2017
modified by rizzi1 on 29 Jun 2020


Published Paper

Inserted: 31 aug 2017
Last Updated: 29 jun 2020

Journal: Potential Anal.
Volume: 53
Pages: 89-112
Year: 2020
Doi: 10.1007/s11118-018-09760-w

ArXiv: 1708.09626 PDF


We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. As a consequence, we show that the intrinsic sub-Laplacian (i.e. defined w.r.t. Popp's measure) is essentially self-adjoint on the equiregular connected components of a sub-Riemannian manifold. This result holds under mild regularity assumptions of the singular region, and when the latter does not contain characteristic points.