Change search
ReferencesLink to record
Permanent link

Direct link
A geometrical version of Hardy's inequality for W01,p(Ω)
Stockholm University, Faculty of Science, Department of Mathematics.
2004 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 8, 2265-2271 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2004. Vol. 132, no 8, 2265-2271 p.
National Category
URN: urn:nbn:se:su:diva-23955OAI: diva2:196097
Available from: 2005-08-24 Created: 2005-08-24 Last updated: 2013-11-18Bibliographically approved
In thesis
1. Improved Lp Hardy Inequalities
Open this publication in new window or tab >>Improved Lp Hardy Inequalities
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).

The aim of this article is to prove a Hardy-type inequality, concerning functions in W_0^{1,p}(D) for some domain D in R^n, involving the volume of D and the distance to the boundary of D. The inequality is a generalization of a previously proved inequality by M. and T. Hoffmann-Ostenhof and A. Laptev, which dealt with the special case p=2.

Paper 2 : A Hardy inequality in the Half-space.

Here we prove a Hardy-type inequality in the half-space which generalize an inequality originally proved by V. Maz'ya to the so-called L^p case. This inequality had previously been conjectured by the mentioned author. We will also improve the constant appearing in front of the reminder term in the original inequality (which is the first improved Hardy inequality appearing in the litterature).

Paper 3 : Hardy type inequalities for Many-Particle systems.

In this article we prove some results about the constants appearing in Hardy inequalities related to many particle systems. We show that the problem of estimating the best constants there is related to some interesting questions from Geometrical combinatorics. The asymptotical behaviour, when the number of particles approaches infinity, of a certain quantity directly related to this, is also investigated.

Paper 4 : Various results in the theory of Hardy inequalities and personal thoughts.

In this article we give some further results concerning improved Hardy inequalities in Half-spaces and other conic domains. Also, some examples of applications of improved Hardy inequalities in the theory of viscous incompressible flow will be given.

Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen, 2005. 18 p.
Spectral theory, Hardy inequality
National Category
urn:nbn:se:su:diva-615 (URN)91-7155-093-3 (ISBN)
Public defence
2005-09-21, sal 14, hus 5, Kräftriket, Stockholm, 10:00
Available from: 2005-08-24 Created: 2005-08-24Bibliographically approved

Open Access in DiVA

No full text

By organisation
Department of Mathematics
In the same journal
Proceedings of the American Mathematical Society

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

Total: 168 hits
ReferencesLink to record
Permanent link

Direct link