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	Integral representation theorem for lower semicontinuous envelopes of integral functionals
	Li, Zhiping
	1998
英文摘要	In the calculus of variations, the problem of minimizing an integral functional F(u; ??) = ??? f(x, u(x), Du(x)) dx, (1.1) on a set of admissible functions A = {u??W1,p(??; Rm): u = u0 on &part??}, (1.2) where ???Rn is a bounded open set with Lipschitz continuous boundary &part?? and 1&lep?? qq(x, u(x), Du(x)) dx, (1.3). on A, where qq(x,s,·) is the quasiconvex envelop of f(x,s,·). The solutions to the two problems coincide whenever qq(·, ??3) happens to be the sequentially weakly lower semicontinuous envelope of F(·, ??). The relationship between the quasiconvex envelopes of f and f?? is discussed. It will show how the sequentially weakly lower semicontinuous envelope of F(?? ????) relates to those of F??(?? ????).; SCI(E); EI; 0; ARTICLE; 4; 541-548; 32
语种	英语
出处	EI
出版者	nonlinear analysis theory methods and applications
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/163334]
专题	数学科学学院
推荐引用方式 GB/T 7714	Li, Zhiping. Integral representation theorem for lower semicontinuous envelopes of integral functionals. 1998-01-01.

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