Poincaré duality for $$L^p$$ cohomology on subanalytic singular spaces

Abstract We investigate the problem of Poincaré duality for $$L^p$$ L p differential forms on bounded subanalytic submanifolds of $$\mathbb {R}^n$$ R n (not necessarily compact). We show that, when p is sufficiently close to 1 then the $$L^p$$ L p cohomology of such a submanifold is isomorphic to its singular homology. In the case where p is large, we show that $$L^p$$ L p cohomology is dual to intersection homology. As a consequence, we can deduce that the $$L^p$$ L p cohomology is Poincaré dual to $$L^q$$ L q cohomology, if p and q are Hölder conjugate to each other and p is sufficiently large.