Universal extension for Sobolev spaces of differential forms and applications

Abstract: This article is devoted to the construction of a family of universal extension operators for the Sobolev spaces of differential forms of degree l () in a Lipschitz domain (, ) for any . It generalizes the construction of the first universal extension operator for standard Sobolev spaces , , on Lipschitz domains, introduced by Stein [E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, NJ, 1970, Theorem 5, p. 181]. We adapt Steinʼs idea in the form of integral averaging over the pullback of a parametrized reflection mapping. The new theory covers extension operators for and in as special cases for , respectively. Of considerable mathematical interest in its own right, the new theoretical results have many important applications: we elaborate existence proofs for generalized regular decompositions. [Copyright &y& Elsevier]