Form boundedness of the general second order differential operator
| dc.creator | Maz'ya, V. G. | |
| dc.creator | Verbitsky, I. E. | |
| dc.date | 2004-11-09 | |
| dc.date.accessioned | 2026-07-07T05:14:10Z | |
| dc.date.available | 2026-07-07T05:14:10Z | |
| dc.description | 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). | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0411216 | |
| dc.identifier | http://arxiv.org/abs/math/0411216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73172 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 35J05 (Primary) 35J10, 42B20, 46E35 (Secondary) | |
| dc.title | Form boundedness of the general second order differential operator | |
| dc.type | text |