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Journal article

Regularity for elliptic systems of differential forms and applications

We prove existence and up to the boundary regularity estimates in L-p and Holder spaces for weak solutions of the linear system delta (Ad omega) + B-T d delta (B omega) = lambda B omega + f in Omega, with either nu boolean AND omega and nu boolean AND delta (B omega) or nu(sic)B omega and nu(sic) (Ad omega) prescribed on partial derivative Omega. 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 Lopatinskii-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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