An estimate on the heat kernel of magnetic Schrodinger operators and uniformly elliptic operators with non-negative potentials

The paper studies the heat kernel of the Schrodinger operator with magnetic fields and of uniformly elliptic operators with non-negative electric pote ntials in the reverse Holder class which includes nonnegative polynomials a s typical examples. The main aim of the paper is to give a pointwise estima te of the heat kernel of the operators above which is affected by magnetic fields and non-negative degenerate electric potentials. A weighted smoothin g estimate for the semigroup generated by the operators above is also given .