报告题目：Geometrically distinct solutions given by symmetries of variational problems with the O(N) -symmetry
报告人：Wacław Marzantowicz教授
报告时间：2019年11月21日上午10:00
报告地点：10号楼415会议室
报告摘要：Abstract. For variational problems with O(N)-symmetry the existence of several geometrically distinct solutions has been shown by use of group theoretic approach in previous articles. It was done by a crafty choice of a family Hi ⊂ O(N) subgroups such that the fixed point subspaces EHi ⊂ E of the action in a corresponding functional space are linearly independent, next restricting the problem to each EHi and using the Palais symmetry principle. In this work we give a thorough explanation of this approach showing a correspondence between the equivalence classes of such subgroups, partial orthogonal flags in RN, and unordered partitions of the number N. By showing that spaces of functions invariant with respect to different classes of groups are linearly independent we prove that the amount of series of geometrically distinct solutions obtained in this way grows exponentially in N, in contrast to logarithmic, and linear growths of earlier papers.
报告人简介：Wacław Marzantowicz教授，波兰数学学会主席，密兹凯维奇大学教授。主要研究方向：非线性分析中的拓扑理论，复分析，G-等价拓扑，不动点理论及偏微分方程。发表重要学术论文60余篇。
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