The Infinity Laplacian Eigenvalue Problem: Reformulation and a Numerical Scheme

Bozorgnia F, Bungert L, Tenbrinck D (2024)


Publication Language: English

Publication Status: Submitted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2024

Journal

Book Volume: 98

Article Number: 40

URI: https://link.springer.com/article/10.1007/s10915-023-02425-w

DOI: 10.1007/s10915-023-02425-w

Open Access Link: https://link.springer.com/content/pdf/10.1007/s10915-023-02425-w.pdf

Abstract

In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the equivalence of the new formulation to the traditional one. Subsequently, we present consistent monotone schemes to approximate infinity ground states and higher eigenfunctions on grids. We prove that our method converges (up to a subsequence) to a viscosity solution of the eigenvalue problem, and perform numerical experiments which investigate theoretical conjectures and compute eigenfunctions on a variety of different domains.

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APA:

Bozorgnia, F., Bungert, L., & Tenbrinck, D. (2024). The Infinity Laplacian Eigenvalue Problem: Reformulation and a Numerical Scheme. Journal of Scientific Computing, 98. https://dx.doi.org/10.1007/s10915-023-02425-w

MLA:

Bozorgnia, Farid, Leon Bungert, and Daniel Tenbrinck. "The Infinity Laplacian Eigenvalue Problem: Reformulation and a Numerical Scheme." Journal of Scientific Computing 98 (2024).

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