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Improved Lp Hardy Inequalities
Stockholm University, Faculty of Science, Department of Mathematics.
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.
Keyword [en]
Spectral theory, Hardy inequality
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-615ISBN: 91-7155-093-3 (print)OAI: oai:DiVA.org:su-615DiVA: diva2:196101
Public defence
2005-09-21, sal 14, hus 5, Kräftriket, Stockholm, 10:00
Opponent
Supervisors
Available from: 2005-08-24 Created: 2005-08-24Bibliographically approved
List of papers
1. A geometrical version of Hardy's inequality for W01,p(Ω)
Open this publication in new window or tab >>A geometrical version of Hardy's inequality for W01,p(Ω)
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
National Category
Mathematics
Identifiers
urn:nbn:se:su:diva-23955 (URN)
Available from: 2005-08-24 Created: 2005-08-24 Last updated: 2017-12-13Bibliographically approved
2. A Hardy inequality in the half-space
Open this publication in new window or tab >>A Hardy inequality in the half-space
2005 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 221, no 2, 482-495 p.Article in journal (Refereed) Published
National Category
Mathematics
Identifiers
urn:nbn:se:su:diva-23956 (URN)
Available from: 2005-08-24 Created: 2005-08-24 Last updated: 2017-12-13Bibliographically approved
3. Geometric many particle Hardy inequalities
Open this publication in new window or tab >>Geometric many particle Hardy inequalities
Manuscript (Other academic)
Identifiers
urn:nbn:se:su:diva-23957 (URN)
Note
Part of urn:nbn:se:su:diva-615Available from: 2005-08-24 Created: 2005-08-24 Last updated: 2010-01-13Bibliographically approved
4. Various results in the theory of Hardy inequalities and personal thoughts
Open this publication in new window or tab >>Various results in the theory of Hardy inequalities and personal thoughts
Manuscript (Other academic)
Identifiers
urn:nbn:se:su:diva-23958 (URN)
Note
Part of urn:nbn:se:su:diva-615Available from: 2005-08-24 Created: 2005-08-24 Last updated: 2010-01-13Bibliographically approved

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