Weighted spectral gap for magnetic Schrödinger operators with a potential term
2009 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 31, no 3, 215-226 p.Article in journal (Refereed) Published
We prove that singular Schrodinger equations with external magnetic field admit a representation with a positive Lagrangian density whenever their "nonmagnetic" counterpart is nonnegative. In this case the operator has a weighted spectral gap as long as the strength of the magnetic field is not identically zero. We provide estimates of the weight in the spectral gap, including the versions with L (p) -norm and with a magnetic gradient term, and applications to an increase of the best Hardy constant due to the presence of a magnetic field. The paper also shows existence of the ground state for the nonlinear magnetic Schrodinger equation with the periodic magnetic field.
Place, publisher, year, edition, pages
2009. Vol. 31, no 3, 215-226 p.
Schrodinger equation, External magnetic field, Positive solutions, Spectral gap, Ground state
IdentifiersURN: urn:nbn:se:uu:diva-120897DOI: 10.1007/s11118-009-9132-xISI: 000269915200002OAI: oai:DiVA.org:uu-120897DiVA: diva2:304117