News & Events
Speaker: Zhou Xiaodan, assistant professor, Okinawa Institute of Science and Technology, Japan
Date: October 20, 2023
Location: Tencent Meeting 546-172-078
Sponsor: Frontiers Science Center for Nonlinear Expectations, Shandong University; Research Centre for Mathematics and Interdisciplinary Sciences Centre, Shandong University; Sino-Russian Mathematics Center in Qingdao
In Euclidean space Rn, a result of Kichenassamy and Veron shows that the n-Laplace operator admits a unique global Green function, i.e., there is a unique, properly normalized singular solution which blows up to +∞at the origin and converges to−∞at infinity. Their proof of uniqueness includes the p-Laplacian Lp in the range 1 < p≤n and is based on C1,αestimates for p-harmonic functions. The argument was later simplified and extended to the Riemannian and Carnot group setting, and thus establishing uniqueness of Green functions in the conformal case p = n in these geometries. The purpose of this talk is to extend this uniqueness result to the setting of complete metric spaces (X, d,μ) equipped with an Ahlfors regular Borel measureμ, and a Poincare inequality. This is a joint work with Mario Bonk and Luca Capogna.
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