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arXiv · 2309.06823

Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials

Lucrezia Cossetti·Luca Fanelli·David Krejcirik
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Abstract

We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover critical Rellich-type potentials too. As a byproduct we obtain uniform resolvent estimates in weighted spaces. Some of the results are new also in the self-adjoint setting.

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Lucrezia Cossetti, Luca Fanelli, David Krejcirik. 2023-09-13. Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials. https://arxiv.org/abs/2309.06823

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