SCHRÖDINGER OPERATORS WITH UNBOUNDED DRIFT
Wolfgang Arendt, Giorgio Metafune, Diego Pallara · 2006
Let aij ∈ C1 b(R N), i, j = 1, . . . ,N be uniformly elliptic, and let b ∈ C1(RN), V ∈ C(RN). If div b p 6 V, then we construct a unique minimal positive semigroup generated by a restriction of the operator A defined by the expression Au = N ∑ i,j=1 Di(aijDju)− N ∑ i=1 biDiu−Vu on Lp(RN) with maximal domain. We give a criterion for C∞ c (RN) to be a core and we give conditions on V and b which imply that the semigroup is given by kernels allowing an upper Gaussian bound. By a specific example we show that our criteria are close to optimal.