Relaxation and Nonoccurrence of the Lavrentiev Phenomenon for Nonconvex Problems  

作　　者：Farhad HSSEINOV 

机构地区：[1]Department of Economics, Bilkent University

出　　处：《Acta Mathematica Sinica,English Series》2013年第6期1185-1198,共14页数学学报（英文版）

摘　　要：The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, the integral of a variational problem must satisfy a classical growth condition, unlike the case of uniform convergence. The relaxations constructed here imply the existence of a Lipschitz convergent minimizing sequence. Based on this observation, the paper also shows that the Lavrentiev phenomenon does not occur for a class of nonconvex problems.The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, the integral of a variational problem must satisfy a classical growth condition, unlike the case of uniform convergence. The relaxations constructed here imply the existence of a Lipschitz convergent minimizing sequence. Based on this observation, the paper also shows that the Lavrentiev phenomenon does not occur for a class of nonconvex problems.

关 键 词：Multidimensional variational problem RELAXATION Lavrentiev phenomenon 

分 类 号：O189.11[理学—数学]