报告题目：On the classification of entire solutions to the critical p-Laplace equation

报告摘要：In this talk, we will focus on the classification of positive solutions to the critical p-Laplace equation. It is well known that such issue is crucial in many applications such as a priori estimates, blow-up analysis and asymptotic analysis. Note that for the subcritical case, the equations have no positive solutions by the well known works of Gidas-Spruck [CPAM1981] and Serrin-Zou [ACTA2002]. While for the critical case, there are nontrivial 2-parameters family of solutions and which are classified  by Caffarelli-Gidas-Spruck [CPAM1989] for p=2 , and by J. Vetois [JDE2016] (for 1<p<2) and B. Sciunzi [Adv.Math.2016](for 2<p<n) under the additional assumption of finite energy. Then by exploiting the method of integral estimate, we obtain the same classification results for (n+1)/3<p<n without any further assumption.

报告人简介：欧乾忠，广西师范大学数学与统计学院教授，广西高等学校优秀人才资助计划获得者。2008年毕业于华东师范大学数学系，获博士学位。主要从事非线性椭圆偏微分方程理论研究，在非线性椭圆偏微分方程解的凸性与刘维尔定理等方面完成了一系列高水平的工作；主要成果发表在Comm. Pure and Appl. Math.、Trans. Amer. Math. Soc.、Journal Geometry Analysis、Adv. Math.等国际著名期刊上。主持完成国家自然科学基金项目2项，主持国家自然科学基金重点专项项目子课题1项。

报告时间：2024年07月04日 10:00-11:00

报告地点：同析4号楼 322会议室