Regularity for elliptic systems of differential forms and applications
Résumé
We prove existence and up to the boundary regularity estimates in L p and Hölder spaces for weak solutions of the linear system δ (Adω) + B T dδ (Bω) = λBω + f in Ω, with either ν ∧ ω and ν ∧ δ (Bω) or νBω and ν (A(x)dω) prescribed on ∂Ω. The proofs are in the spirit of 'Campanato method' and thus avoid potential theory and do not require a verification of Agmon-Douglis-Nirenberg or Lopatinski-Shapiro type conditions. Applications to a number of related problems , such as general versions of the time-harmonic Maxwell system, stationary Stokes problem and the 'div-curl' systems, are included.
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