Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics

Lashi Bandara; Hemanth Saratchandran

doi:10.1016/j.jfa.2017.09.001

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arXiv · 1606.06190

Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics

Lashi Bandara·Hemanth Saratchandran

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Abstract

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.

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BibTeX RIS

Lashi Bandara, Hemanth Saratchandran. 2016-06-20. Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics. https://doi.org/10.1016/j.jfa.2017.09.001

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