Abstract
The paper studies the heat kernel of the Schrödinger operator with magnetic fields and of uniformly elliptic operators with non-negative electric potentials in the reverse Hölder class which includes non-negative polynomials as typical examples. The main aim of the paper is to give a pointwise estimate of the heat kernel of the operators above which is affected by magnetic fields and non-negative degenerate electric potentials. A weighted smoothing estimate for the semigroup generated by the operators above is also given.
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