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【网络讲座】李亦:Monotone Properties of the Eigenfunction of Neumann Problems(时间5.22)
【 作者:  校对时间:2020年05月18日 08:26  访问次数: 】

讲座人:李亦 教授

讲座时间:5月22日9:00

讲座地点:ZOOM会议ID:95043840434  密码:123456

主办单位:数学与统计学院

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  In this paper, we prove the hot spots conjecture for long rotationally symmetric domains in Rn by the continuity method. More precisely, we show that the odd Neumann eigenfunction in xn associated with lowest nonzero eigenvalue is a Morse function on the boundary, which has exactly two critical points and is monotone in the direction from its minimum point to its maximum point. As a consequence, we prove that the Jerison and Nadirashvili`s conjecture 8.3 holds true for rotationally symmetric domains and are also able to obtain a sharp lower bound for the Neumann eigenvalue. This is a joint work with Prof. Hongbin Chen and Prof. Lihe Wang, which appear in Journal de Mathematiques Pures et Appliquees 2019.10.1