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arXiv · 1708.09626

On the essential self-adjointness of singular sub-Laplacians

Valentina Franceschi·Dario Prandi·Luca Rizzi
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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 on the singular region, and when the latter does not contain characteristic points.

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Valentina Franceschi, Dario Prandi, Luca Rizzi. 2019-01-08. On the essential self-adjointness of singular sub-Laplacians. https://doi.org/10.1007/s11118-018-09760-w

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