Form boundedness of the general second order differential operator

Details Form boundedness of the general second order differential operator Form boundedness of the general second order differential operator

2004-11-09

arxiv.org/abs/math/0411216v1

Mathematics

Analysis of PDEs

43 pages

Scientific paper

We 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).

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