I am doing a research on a certain type of operator, and in the course of it I need to determine the following: Given the operator $D$ below, and identity operator $I$, $ D=\begin{pmatrix} 0 & -\text{div}\,A \\ \nabla & 0 \\ \end{pmatrix} $ where $A$ is a certain operator which is not important here, can I get an explicit expression for its resolvent $(\lambda I- D)^{-1}$ ?
Thank you.