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Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation

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Abstract

We consider a self-adjoint fourth-order operator with real 1-periodic coefficients on the unit interval and the Neumann–Dirichlet boundary conditions. The spectrum of this operator is discrete. We determine the high energy asymptotics for the eigenvalues and a trace formula for this operator.

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Funding

This work was partially supported by the grant MK-160.2022.1.1 of the President of Russian Federation for young candidates of sciences

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  1. Southern Mathematical Institute, Vladikavkaz Scientific Center of RAS, 53 Vatutin Str., Vladikavkaz, Russia, 362025

    Dmitry M. Polyakov

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  1. Dmitry M. Polyakov
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Correspondence to Dmitry M. Polyakov.

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Communicated by Gerald Teschl.

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Polyakov, D.M. Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation. Monatsh Math 202, 171–212 (2023). https://doi.org/10.1007/s00605-022-01808-9

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