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arXiv · 2505.22329

Finsler $p$-Laplacian in domains becoming unbounded

Luca Esposito·Lorenzo Lamberti·Dattatreya N. N.·Prosenjit Roy
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Abstract

We study the asymptotic behavior of sequences of solutions, energies functionals, and the first eigenvalues associated with the Finsler $p$-Laplace operator, also known as the anisotropic $p$-Laplace operator on a sequence of bounded cylinders whose length tends to infinity. We prove that the solutions on the bounded cylinders converge to the solution on the cross-section, with a polynomial rate of convergence in the general case and exponential convergence in some special cases. We show that energies on finite cylinders, with the multiplication of a scaling factor, converge to the energy on the cross-section. Finally, we investigate the convergence of the first eigenvalue and, for a specific subclass, we provide the optimal convergence rate.

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Luca Esposito, Lorenzo Lamberti, Dattatreya N. N., Prosenjit Roy. 2025-05-28. Finsler $p$-Laplacian in domains becoming unbounded. https://arxiv.org/abs/2505.22329

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