Self-Adjointness, m -Accretivity, and Separability for Perturbations of Laplacian and Bi-Laplacian on Riemannian Manifolds
Let Δ A and ΔA2 be the magnetic Laplacian and magnetic bi-Laplacian (with a smooth magnetic field A) on a geodesically complete Riemannian manifold M and let V be a real-valued function on M. We give a sufficient condition for the essential self-adjointness of Δ A+ V on the space of smooth compactly supported functions on M. Additionally, we provide sufficient conditions for the m-accretivity of the operator sum TΔA(p)+TV(p) and the self-adjointness of TΔA2(2)+TV(2), where TΔA(p), TΔA2(p), TV(p) are the “maximal” operators in Lp(M) , 1 < p< ∞, corresponding to Δ A, ΔA2, and V. As a consequence of these results, we obtain the separation property for Δ A+ V in Lp(M) and the same property for ΔA2+V in L2(M). In some results pertaining to ΔA2+V, we assume that the Ricci curvature of M is bounded from below by a (possibly unbounded) non-positive function depending on the distance from a reference point.
Integral Equations and Operator Theory
Digital Object Identifier (DOI)
Milatovic. (2018). Self-Adjointness, m-Accretivity, and Separability for Perturbations of Laplacian and Bi-Laplacian on Riemannian Manifolds. Integral Equations and Operator Theory, 90(2), 1–21. https://doi.org/10.1007/s00020-018-2452-8