Abstract
We obtain lower bounds for the magnetic Dirichlet form in dimensions d≥2. For d=2 the results generalize a well known lower bound by the magnetic field strength: we replace the actual magnetic field Bby an non-vanishing effective field which decays outside the support of Bas dist(x,suppB)−2. In the case d≥3 we establish that the magnetic form is bounded from below by the magnetic field strength, if one assumes that the field does not vanish and its direction is slowly varying.
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Balinsky, A., Laptev, A. & Sobolev, A.V. Generalized Hardy Inequality for the Magnetic Dirichlet Forms. Journal of Statistical Physics 116, 507–521 (2004). https://doi.org/10.1023/B:JOSS.0000037228.35518.ca
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DOI: https://doi.org/10.1023/B:JOSS.0000037228.35518.ca