Sobolev regularity of quasiconformal mappings on domains

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© 2019, The Hebrew University of Jerusalem. Consider a Lipschitz domain Ω and a measurable function μ supported in Ω ¯ with ‖μ‖L∞ < 1. Then the derivatives of a quasiconformal solution of the Beltrami equation ∂¯f=μ∂f inherit the Sobolev regularity Wn,p(Ω) of the Beltrami coefficient μ as long as Ω is regular enough. The condition obtained is that the outward unit normal vector N of the boundary of the domain is in the trace space, that is, N∈Bp,pn−1/p(∂Ω).
Original languageEnglish
Pages (from-to)513-562
JournalJournal d'Analyse Mathematique
Publication statusPublished - 1 Oct 2019


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