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Generalized Hardy inequality for the magnetic Dirichlet forms
KTH, Superseded Departments, Mathematics.
2004 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 116, no 4-Jan, 507-521 p.Article in journal (Refereed) Published
Abstract [en]

We obtain lower bounds for the magnetic Dirichlet form in dimensions d greater than or equal to 2. For d = 2 the results generalize a well known lower bound by the magnetic field strength: we replace the actual magnetic field B by an non-vanishing effective field which decays outside the support of B as dist( x, supp B)(-2). In the case d greater than or equal to 3 we establish that the magnetic form is bounded from below by the magnetic field strength, if one assumes that the field does not vanish and its direction is slowly varying.

Place, publisher, year, edition, pages
2004. Vol. 116, no 4-Jan, 507-521 p.
Keyword [en]
magnetic field, Dirichlet forms, the Hardy inequality, schrodinger-operators
National Category
URN: urn:nbn:se:kth:diva-23635DOI: 10.1023/B:JOSS.0000037228.35518.caISI: 000223177200023ScopusID: 2-s2.0-4344647047OAI: diva2:342334
QC 20100525 QC 20110926Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2011-09-26Bibliographically approved

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Laptev, Ari
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