ON THE CONTRACTION PROPERTIES FOR WEAK SOLUTIONS TO LINEAR ELLIPTIC EQUATIONS WITH L2-DRIFTS OF NEGATIVE DIVERGENCE

We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with L2 -drifts of negative divergence and singular zero -order terms which are positive. Our main target is to show the Lr-contraction properties of the unique weak solutions. Indeed, using the Dirichlet form theory, we construct a sub-Markovian C0 -resolvent of contractions and identify it to the weak solutions. Furthermore, we derive an L1 -stability result through an extended version of the L1 -contraction property.