MINIMIZERS AND SYMMETRIC MINIMIZERS FOR PROBLEMS WITH CRITICAL SOBOLEV EXPONENT

被引:2
作者
Waliullah, Shoyeb [1 ]
机构
[1] Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden
关键词
Concentration-compactness principle; critical Sobolev exponent; symmetric solutions of elliptic equations; Sobolev embeddings in weighted spaces; CONCENTRATION-COMPACTNESS PRINCIPLE; ELLIPTIC-EQUATIONS; SHARP CONSTANTS; CRITICAL GROWTH; INEQUALITIES; EXISTENCE; CALCULUS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we will be concerned with the existence and nonexistence of constrained minimizers in Sobolev spaces D-k,D-p (R-N), where the constraint involves the critical Sobolev exponent. Minimizing sequences are not, in general, relatively compact for the embedding D-k,D-p(R-N) hooked right arrow L-p*(R-N, Q) when Q is a non-negative, continuous, bounded function. However if Q has certain symmetry properties then all minimizing sequences are relatively compact in the Sobolev space of appropriately symmetric functions. For Q which does not have the required symmetry, we give a condition under which an equivalent norm in D-k,D-p(R-N) exists so that all minimizing sequences are relatively compact. In fact we give an example of a Q and an equivalent norm in D-k,D-p(R-N) so that all minimizing sequences are relatively compact.
引用
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页码:291 / 326
页数:36
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