Let X be a singular complex space. Roughly speaking, by definition, one says that the L2-Stokes-Theorem holds on X for the exterior derivative d or for the $\overline{\partial}$-operator, respectively, if partial integration is possible with respect to these operators on L2-forms, i.e., the singular set should be negligible in a certain sense. It is conjectured, that the L2-Stokes-Theorem holds for d on projective varieties, and it is known to fail in general for $\overline{\partial}$. In this talk, we will discuss the state of the art and present an idea of how to overcome the problem for the $\overline{\partial}$-operator.