Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics
Artikel i vetenskaplig tidskrift, 2017

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential self-adjointness of such operators to a negligible boundary property. When the operator possesses higher regularity coefficients, we show that higher powers are essentially self-adjoint if and only if this condition is satisfied. In the case that the low-regularity Riemannian metric induces a complete length space, we demonstrate essential self-adjointness of the operator and its higher powers up to the regularity of its coefficients. We also present applications to Dirac operators on Dirac bundles when the metric is non-smooth.

Rough metric

Essential self-adjointness

Negligible boundary

Elliptic operator


Menaka Lashitha Bandara

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

H. Saratchandran

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 273 3719-3758