Crystallization of polylactide films: An atomic force microscopy study of the effects of temperature and blending
- 作者：Yury Yuryev ; Paula Wood-Adams ; Marie-Claude Heuzey ; Charles Dubois ; Joseé ; Brisson
- 关键词：Perturbed optimization problem ; Strictly convex space ; Kadec space ; Well-posedness ; none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4SM1TKF-5&_mathId=mml18&_user=1067359&_cdi=6894&_rd
- 刊名：Polymer
- 出版年：2008
- 期刊代码：83_00323861
- 类别：ms
- 出版时间：29 April 2008
- 卷：49
- 期：9
- 页码：2306-2320
- 文件大小：2511 K
摘要
Let X be a Banach space and Z a nonempty subset of X. Let 
be a lower semicontinuous function bounded from below and p
1. This paper is concerned with the perturbed optimization problem of finding z0
Z such that 
x−z0p+J(z0)=infzZ{x−zp+J(z)}, which is denoted by minJ(x,Z). The notions of the J-strictly convex with respect to Z and of the Kadec with respect to Z are introduced and used in the present paper. It is proved that if X is a Kadec Banach space with respect to Z and Z is a closed relatively boundedly weakly compact subset, then the set of all xX for which every minimizing sequence of the problem minJ(x,Z) has a converging subsequence is a dense Gδ-subset of X
Z0, where 13d0f1d4613dac362b8d714218" title="Click to view the MathML source" alt="Click to view the MathML source">Z0 is the set of all points zZ such that z is a solution of the problem minJ(z,Z). If additionally p>1 and X is J-strictly convex with respect to Z, then the set of all xX for which the problem minJ(x,Z) is well-posed is a dense Gδ-subset of d02b498c61e" title="Click to view the MathML source" alt="Click to view the MathML source">XZ0.
1. This paper is concerned with the perturbed optimization problem of finding z0Z such that x−z0p+J(z0)=infzZ{x−zp+J(z)}, which is denoted by minJ(x,Z). The notions of the J-strictly convex with respect to Z and of the Kadec with respect to Z are introduced and used in the present paper. It is proved that if X is a Kadec Banach space with respect to Z and Z is a closed relatively boundedly weakly compact subset, then the set of all xX for which every minimizing sequence of the problem minJ(x,Z) has a converging subsequence is a dense Gδ-subset of XZ0, where 13d0f1d4613dac362b8d714218" title="Click to view the MathML source" alt="Click to view the MathML source">Z0 is the set of all points zZ such that z is a solution of the problem minJ(z,Z). If additionally p>1 and X is J-strictly convex with respect to Z, then the set of all xX for which the problem minJ(x,Z) is well-posed is a dense Gδ-subset of d02b498c61e" title="Click to view the MathML source" alt="Click to view the MathML source">XZ0.