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
时 间：2022.11.17（星期四）
地 点：腾讯会议948-3602-5762
n 下午2：00-3：00
报告人：熊昌伟 教授（四川大学）
题 目：Some estimates on an exterior Steklov eigenvalue problem
摘 要：In this talk we will discuss a Steklov eigenvalue problem on an exterior Euclidean domain. We will present sharp lower and upper bounds for its first eigenvalue under various conditions on the domain. Time permitting, we shall discuss an upper bound for its second eigenvalue.
n 下午3：00-4：00
报告人：欧乾忠 教授（广西师范大学）
题 目：On the classification of entire solutions to the critical p-Laplace equation
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 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.
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