Weak Compactness and its Applications

• Main Authors: Yi-Lin Wang, 王一琳
• Other Authors: Chi-Kun Lin
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/60483640978083524991

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 92 === 　　In this paper, we will study the concept of weak convergence and the related topices. First we describe the Riemann-Lebesgue lemma since it is the origin of the weak convergence. In the sequal, in section 2 we dicuss the main properties of weak and weak* convergence in a Banach space. We also details these notions for the particular case of L^p spaces in section 3. Then we will get the weak compactness in L^p spaces. In section 4 we talk a relevant class of periodic oscillating functions, which is the application of weak convergence in L^p spaces. And we will give an example about the weak limit of oscillating periodic functions. In section 5, we introduce some classes of Sobolev spaces and discuss their main properties. Finally, then we will get the compactness result in Sobolev spaces.