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Various results in the theory of Hardy inequalities and personal thoughts
Stockholm University, Faculty of Science, Department of Mathematics.
Manuscript (Other academic)
URN: urn:nbn:se:su:diva-23958OAI: diva2:196100
Part of urn:nbn:se:su:diva-615Available from: 2005-08-24 Created: 2005-08-24 Last updated: 2010-01-13Bibliographically 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

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