In this talk, we discuss the Dirichlet eigenvalue problem associated to the infinity Laplacian in metric spaces. We provide a direct PDE approach to find the principal eigenvalue and eigenfunctions for a bounded domain in a proper geodesic space with no measure structure. We give an appropriate notion of solutions to the infinity eigenvalue problem and show the existence of solutions by adapting Perron's method. Our method is different from the standard limit process, introduced by Juutinen-Lindqvist-Manfredi (ARMA,1999), via the variational eigenvalue formulation for $p$-Laplacian in the Euclidean space. Several further results and concrete examples will be given in the case of finite metric graphs. This talk is based on joint work with Ayato Mitsuishi at Fukuoka University.

2021年11月12日
9am - 10am
地點
https://hkust.zoom.us/j/98685800264 (Passcode: 440023)
講者/表演者
Prof. Qing LIU
Fukuoka University, Japan
主辦單位
Department of Mathematics
聯絡方法
付款詳情
對象
Alumni, Faculty and staff, PG students, UG students
語言
英語
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