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.

12 Nov 2021
9am - 10am
Where (Passcode: 440023)
Prof. Qing LIU
Fukuoka University, Japan
Department of Mathematics
Payment Details
Alumni, Faculty and staff, PG students, UG students
Other Events
9 Dec 2021
Seminar, Lecture, Talk
Department of Mathematics - Seminar on FinTech and Machine Learning - Problems and probable solutions of applying recent machine learning techniques to financial time series and data
Recent machine learning techniques such as deep learning and reinforcement learning were built on specific assumptions of the underlying data generation process.  Fi...
6 Dec 2021
Seminar, Lecture, Talk
Department of Chemistry - PhD Student Seminar - Soy Sauce: An Insight into the Health Benefits and Risks
Student: Miss Yao ZHAO Department: Department of Chemistry, HKUST Supervisor: Professor Wan CHAN