主講者:	1.李天虹教授 (中國科學院數學與系統科學院) 2.陳國璋教授 (清華大學)
講題:	1.On the space of $L^p$ Young measure 2.Some remarks on convex and concave central configurations
時間:	2010-05-18 (Tue.)  15:00 - 16:50
地點:	數學所 617 研討室 (台大院區)
Abstract:	1. In a paper of Joly-Metivier-Rauch [JMR], they study properties of $L^p$-sequences on an open subset of $R^n$ with boundary having zero measure with some applications in partial differential equations. We consider $L^p$-sequences on any set $X$ with a $\sigma$-algebra and a $\sigma$-finite, atom free complete measure such that its $L^1$ space is separable. We give a sufficient and necessary condition for a Young measure: $X\rightarrow \mbox{prob }(S^n)$ to be the limit of a bounded sequence in $L^p(X, R^n)$ with $1\leq p \leq \infty$. Then we prove a theorem which generalizes an important proposition of [JMR]. This is a joint work with B.H.Li. 2. It is well-known that the planar four-body problem has at least 6 convex central configurations and 14 concave central configurations. Not much is known about the case of five or more bodies. In this talk I will briefly discuss this problem and its analogy in the spatial problem, and show some examples of central configurations which are both convex and concave. This is a joint work with J.S.Hsiao.
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