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    In this paper, we prove a div–curl type theorem in the Heisenberg group ℍ1, and then we develop a theory of H-convergence for second order differential operators in divergence form in ℍ1. The div–curl theorem requires an intrinsic notion of the curl operator in ℍ1 (that we denote by curl), that turns out to be a second order differential operator in the left invariant horizontal vector fields. As an evidence of the coherence of this definition, we prove an intrinsic Stokes formula for curl. Eventually, we show that this notion is related to one of the exterior differentials in Rumin's complex on contact manifolds.

    AMSC: 35B27, 74Q99, 43A80, 26B20


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