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Form boundedness of the general second-order differential operator
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Columbia University, Missouri.
2006 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 59, no 9, 1286-1329 p.Article in journal (Refereed) Published
Abstract [en]

We give explicit necessary and sufficient conditions for the boundedness of the general second-order differential operator ℒ = ∑ i,j=ln aij∂i∂j + ∑j=1nbj∂j+c with real- or complex-valued distributional coefficients aij, bj, and c, acting from the Sobolev space W1, 2(ℝn) to its dual W-1, 2(ℝn). This enables us to obtain analytic criteria for the fundamental notions of relative form boundedness, compactness, and infinitesimal form boundedness of C with respect to the Laplacian on L 2(ℝn). In particular, we establish a complete characterization of the form boundedness of the Schrödinger operator (i ▽, + a→)2 + q with magnetic vector potential a→ ∈ Lloc2(ℝn)n and q ∈ D′(ℝn). © 2006 Wiley Periodicals, Inc.

Place, publisher, year, edition, pages
2006. Vol. 59, no 9, 1286-1329 p.
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Mathematics
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URN: urn:nbn:se:liu:diva-35986DOI: 10.1002/cpa.20122Local ID: 29260OAI: oai:DiVA.org:liu-35986DiVA: diva2:256834
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13

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Maz´ya, Vladimir G.

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