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

Lashi Bandara (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori) ; H. Saratchandran
Journal of Functional Analysis (0022-1236). Vol. 273 (2017), 12, p. 3719-3758.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Essential self-adjointness, Elliptic operator, Rough metric, Negligible boundary

Denna post skapades 2017-11-21.
CPL Pubid: 253270


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Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)



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