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Minimizers and symmetric minimizers for problems with critical sobolev exponent
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, ISSN 1230-3429, Vol. 34, no 2, 291-326 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2009. Vol. 34, no 2, 291-326 p.
Keyword [en]
Concentration-compactness principle, critical Sobolev exponent, symmetric solutions of elliptic equations, Sobolev embeddings in weighted spaces
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-59376ISI: 000273066000007OAI: oai:DiVA.org:su-59376DiVA: diva2:429653
Note
authorCount :1Available from: 2011-07-05 Created: 2011-06-27 Last updated: 2011-07-05Bibliographically approved

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