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Dario Prandi

Researcher in control theory and biomimetic image processing.

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On the essential self-adjointness of sub-Laplacians

Valentina Franceschi, Dario Prandi and Luca Rizzi

Abstract: 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.