Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	欧乾忠教授，广西师范大学
Inviter:	邱国寰
Title:	On the classification of entire solutions to the critical p-Laplace equation
Time & Venue:	2022.11.17 15:00-16:00 腾讯会议：948-3602-5762
Abstract:	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 were 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, via the method of moving planes. Then by exploiting the method of integral estimate, we obtain the same classification results for (n+1)/3<p<n without any further assumption.