Intersection de Rham theory on spaces with isolated singularities

We construct an extension of the classical de Rham theory on spaces with isolated singularities, that we call intersection de Rham theory. The construction is based on the definition of some closed extension of the exterior differentiation operator on (distributional) forms, based on the introduction of some boundary conditions at the singular point. We prove that the cohomology of the associated Hilbert complex, that we call intersection de Rham complex, is naturally isomorphic to the combinatorial intersection cohomology of Goresky and MacPherson.