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arXiv · 2401.16576

Homogenization of nonlocal spectral problems

Andrey Piatnitski·Volodymyr Rybalko
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Abstract

We study asymptotic behavior of the bottom point of the spectrum of convolution type operators in environments with locally periodic microstructure. We show that its limit is described by an additive eigenvalue problem for Hamilton-Jacobi equation. In the periodic case we establish a more accurate two-term asymptotic formula.

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Andrey Piatnitski, Volodymyr Rybalko. 2024-01-29. Homogenization of nonlocal spectral problems. https://arxiv.org/abs/2401.16576

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