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arXiv · 2608.16231

Eigenvalue homogenization for the $p-$Laplacian with rapidly oscillating $L^q$ weights

Ariel Salort
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Abstract

In this article, we study the convergence rates of variational eigenvalues of the $p$-Laplacian with rapidly oscillating weights and potentials belonging in a suitable $L^q$ space. Our analysis covers both Dirichlet and Neumann boundary conditions, and we derive explicit estimates in terms of the eigenvalue index $k \in \mathbb{N}$ and the oscillation parameter $\varepsilon > 0$. These results are obtained through a detailed examination of certain oscillatory integrals and extend previously known results in the literature.

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Ariel Salort. 2026-08-17. Eigenvalue homogenization for the $p-$Laplacian with rapidly oscillating $L^q$ weights. https://doi.org/10.1002/mana.70231

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