Form boundedness of the general second order differential operator

dc.creatorMaz'ya, V. G.
dc.creatorVerbitsky, I. E.
dc.date2004-11-09
dc.date.accessioned2026-07-07T05:14:10Z
dc.date.available2026-07-07T05:14:10Z
dc.descriptionWe give explicit necessary and sufficient conditions for the boundedness of the general second order differential operator L with real- or complex-valued distributional coefficients acting from the Sobolev space W^{1,2}(R^n) to its dual W^{-1,2}(R^n). This enables us to obtain analytic criteria for the fundamental notions of relative form boundedness, compactness, and infinitesimal form boundedness of L with respect to the Laplacian on L^2(R^n). In particular, we establish a complete characterization of the form boundedness of the Schroedinger operator (i \nabla + a)^2 + q with magnetic vector potential a \in L^2_{loc} and q \in D'(\R^n).
dc.description43 pages
dc.identifierhttps://arxiv.org/abs/math/0411216
dc.identifierhttp://arxiv.org/abs/math/0411216
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73172
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subject35J05 (Primary) 35J10, 42B20, 46E35 (Secondary)
dc.titleForm boundedness of the general second order differential operator
dc.typetext

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