On weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence

Haesung Lee

Published 2023-02-02Version 1

We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence and singular zero-order terms which are positive. In particular, using Dirichlet form theory we connect a unique solution to the corresponding resolvent and obtain the $L^r$-contraction properties of the unique solution. Furthermore, an elliptic $L^1$-stability is derived through the $L^1$-contraction property.