The Infinity Laplacian Eigenvalue Problem: Reformulation and a Numerical Scheme
Journal of Scientific Computing(2024)
摘要
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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关键词
Infinity Laplacian operator,Infinity ground states,Nonlinear Eigenvalue problems,Monotone schemes
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