Braides, AndreaDal Maso, Gianni2023-05-102023-05-102023-05-09https://openscience.sissa.it/handle/1963/35459Preprint number SISSA/06/2023We prove an integral-representation result for limits of non-local quadratic forms on H1 0 pΩq, with Ω a bounded open subset of Rd, extending the representation on C8c pΩq given by the Beurling-Deny formula in the theory of Dirichlet forms. We give a counterexample showing that a corresponding representation may not hold if we consider analogous functionals in W1,p0 pΩq, with p ‰ 2 and 1 ă p ď d.enΓ-convergenceDirichlet formsnon-local functionalsintegral representationPreprint