中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人：朱梅俊 教授 (Department of Mathematics, University of Oklahoma，USA)
题 目：Divergent operator with degeneracy and related sharp inequalities
时 间：2019.07.01（星期一）, 16 :00-17:00
地 点：数学院南楼N202室
摘 要：We study some nonlinear equations on the half space and obtain the classification results for positive solutions. The differential operator is a divergent operator with degeneracy on the boundary, which is related to the extension operators. The classification results enable us to establish the sharp form for a generalized Gagliardo-Nirenberg inequality, as well as the sharp form for a weighted Sobolev inequalities. Early results on the sharp weighted Sobolev inequalities were obtained by Jerison and Lee, and by Beckner. Our result solves an open question for more than twenty years. This is a joint work with J. Dou, L. Sun and L. Wang.
