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Annali di Matematica Pura ed Applicata

, Volume 169, Issue 1, pp 321–354 | Cite as

Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations

  • Christoph Hamburger
Article

Summary

We prove partial regularity for the vector-valued differential forms solving the system δ(A(x, ω))=0, dω=0, and for the gradient of the vector-valued functions solving the system div A(x, Du)=B(x, u, Du). Here the mapping A, with A(x, w) ≈ (1+ + ¦ω¦2)(p − 2)/2 ω (p⩾2), satisfies a quasimonotonicity condition which, when applied to the gradient A(x, ω)=Dωf(x, ω) of a real-valued functionf, is analogous to but stronger than quasiconvexity for f. The case 1<p<2 for monotone A is reduced to the case p⩾2 by a duality technique.

Keywords

Differential Equation Partial Differential Equation Nonlinear System Differential Form Partial Regularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1995

Authors and Affiliations

  • Christoph Hamburger
    • 1
  1. 1.Mathematisches Institut der Universität BonnBonnGermany

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