uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Cocompactness and minimizers for inequalities of Hardy-Sobolev type involving N-Laplacian
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2010 (English)In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 17, no 4, 467-477 p.Article in journal (Refereed) Published
Abstract [en]

The paper studies quasilinear elliptic problems in the Sobolev spaces W-1,W-p(Omega), Omega subset of R-N, with p = N, that is, the case of Pohozhaev-Trudinger-Moser inequality. Similarly to the case p < N where the loss of compactness in W-1,W-p(R-N) occurs due to dilation operators u bar right arrow t((N-p)/p)u(tx), t > 0, and can be accounted for in decompositions of the type of Struwe's "global compactness" and its later refinements, this paper presents a previously unknown group of isometric operators that leads to loss of compactness in W-0(1,N) over a ball in R-N. We give a one-parameter scale of Hardy-Sobolev functionals, a "p = N"-counterpart of the Holder interpolation scale, for p > N, between the Hardy functional integral vertical bar u vertical bar(p)/vertical bar x vertical bar(p) dx and the Sobolev functional integral vertical bar u vertical bar(pN/(N-mp)) dx. Like in the case p < N, these functionals are invariant with respect to the dilation operators above, and the respective concentration-compactness argument yields existence of minimizers for W-1,W-N-norms under Hardy-Sobolev constraints.

Place, publisher, year, edition, pages
2010. Vol. 17, no 4, 467-477 p.
Keyword [en]
Trudinger-Moser inequality, Elliptic problems in two dimensions, Concentration compactness, Global compactness, Asymptotic orthogonality, Weak convergence, Palais-Smale sequences
National Category
URN: urn:nbn:se:uu:diva-135597DOI: 10.1007/s00030-010-0063-4ISI: 000280641800005OAI: oai:DiVA.org:uu-135597DiVA: diva2:375243
Available from: 2010-12-07 Created: 2010-12-07 Last updated: 2011-03-01Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text
By organisation
Analysis and Applied Mathematics
In the same journal
NoDEA. Nonlinear differential equations and applications (Printed ed.)

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 177 hits
ReferencesLink to record
Permanent link

Direct link