In this paper, we will prove several generalized versions, dependent on different boundary conditions, of the classical Gaffney–Friedrichs inequality for differential forms on Heisenberg groups. In the first part of the paper, we will consider horizontal differential forms and the horizontal differential. In the second part, we shall prove the counterpart of these results in the context of Rumin’s complex.
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Bruno Franchi, Francescopaolo Montefalcone, Elena Serra, Gaffney–Friedrichs inequality for differential forms on Heisenberg groups. Rev. Mat. Iberoam. 35 (2019), no. 3, pp. 643–692DOI 10.4171/RMI/1065