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：2023.09.13（星期三）
地 点：Zoom: 5631334105 code: AMSS
n 上午09 :00-09 :50
报告人：田龙 副教授（南京理工大学）
题 目：Measure estimates of nodal sets of solutions to second-order elliptic equations with the potential term
摘 要：In this talk, we will discuss the upper bound on the measure of the nodal set problem with a potential term V. We will demonstrate some upper bounds on the measure of the nodal set of solutions in both the cases when V is large and when it is small.
n 上午10 :00-10 :50
报告人：蒋飞达 教授（东南大学）
题 目：Keller-Osserman conditions for k-Hessian type equations with gradient terms
摘 要：In this talk, we consider a k-Hessian type equations with gradient terms and provide a necessary and sufficient condition for the solvability of entire admissible subsolutions, which can be regarded as a generalized Keller-Osserman condition. The existence and nonexistence results are proved in different ranges of the parameter, which embrace the standard Hessian equation case as a typical example. The difference between the semilinear case (k = 1) and the fully nonlinear case (k\ge 2) is also concerned.
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