報告題目：Geometrically distinct solutions given by symmetries of variational 

problems with the O(N) -symmetry

報告人：Wac?aw Marzantowicz教授

報告時間：2019年11月21日上午10:00

報告地點：10號樓415會議室

報告摘要：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 ?xed 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 di?erent 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.

報告人簡介：Wac?aw Marzantowicz教授，波蘭數學學會主席，密茲凱維奇大學教授。主要研究方向：非線性分析中的拓撲理論，復分析，G-等價拓撲，不動點理論及偏微分方程。發表重要學術論文60余篇。

理學院

2019年11月18日