中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：Hoai-Minh Nguyen (Sorbonne University)

报告语言：英文

题  目：On Hardy's and Caffarelli, Kohn, Nirenberg's inequalities

时  间：2023.05.30（星期二）16:00-17:00

地  点：Zoom ID: 924 888 5804  Passcode:AMSS2022 

摘  要：I discuss the full range of Caffarelli, Kohn, Nirenberg's inequalities for fractional Sobolev spaces and several improvements of Hardy's and Caffarelli, Kohn, Nirenberg's inequalites for standard integer order Sobolev spaces. The full range extension for radial functions are also mentioned.  Their proofs, which are quite elementary and not involved the integration by parts, are discussed. The talk is based on joint work with Marco Squassina and Arka Mallick.

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题  目：Gagliardo-Nirenberg's inequalities associated with the Coulomb terms and their extensions

时  间：2023.05.31（星期三）16:00-17:00

地  点：Zoom ID: 924 888 5804  Passcode:AMSS2022

摘  要：I will discuss the full range of Gagliardo-Nirenberg's inequalities associated with the Coulomb terms when the derivative s is between 0 and 1. Their extensions in the spirit of  Caffarelli-Kohn-Nirenberg's inequalities are also mentioned.  Their applications in deriving new one body and many body Hardy-Lieb-Thirring's inequalities  are presented. This is joint work with Arka Mallick.