De Rham's theorem for Orlicz cohomology

We prove that the de Rham $L^{\varphi }$-cohomology of a Riemannian manifold $M$ admiting a convenient triangulation $X$ is isomorphic to the simplicial ${\mathrm{\ell }}^{\varphi }$-cohomology of $X$ for any Young function $\varphi$. This result implies the quasi-isometry invariance of the first one.