Previous issue ·  Next issue ·  Most recent issue · All issues

# Journal of Operator Theory

Volume 55, Issue 1, Winter 2006  pp. 185-211.

Schroedinger operators with unbounded drift

Authors Wolfgang Arendt (1), Giorgio Metafune (2), and Diego Pallara (3)
Author institution: (1) Abteilung Angewandte Analysis, Universitaet Ulm, D-89069 Ulm, Germany
(2) Dipartimento di Matematica Ennio de Giorgi'', Universit\a di Lecce, C.P. 193, 73100, Lecce, Italia
Dipartimento di Matematica
(3) Ennio de Giorgi'', Universit\a di Lecce, C.P. 193, 73100, Lecce, Italia

Summary:  Let $a_{ij}\in C_\mathrm b^1(\re^N)$, $i,j=1,\ldots, N$ be uniformly elliptic, and let $b\in C^1(\re^N)$, $V\in C(\re^N)$. If $\frac{\diver{b}}{p}\leqslant V$, then we construct a unique minimal positive semigroup generated by a restriction of the operator $A$ defined by the expression $$Au=\sum_{i,j=1}^N D_i(a_{ij}D_ju) - \sum_{i=1}^N b_iD_iu - Vu$$ on $L^p(\re^N)$ with maximal domain. We give a criterion for $C_\mathrm c^\infty(\re^N)$ 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.

Contents    Full-Text PDF