Quasimonotonicity,regularity and duality for nonlinear systems of partial differential equations |
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Authors: | Christoph Hamburger |
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Institution: | (1) Present address: Mathematisches Institut der Universität Bonn, Beringstraße 4, D-53115 Bonn, Germany |
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Abstract: | Summary We prove partial regularity for the vector-valued differential forms solving the system (A(x, ))=0, d=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+ + ¦¦2)(p – 2)/2 (p2), satisfies a quasimonotonicity condition which, when applied to the gradient A(x, )=Df(x, ) of a real-valued functionf, is analogous to but stronger than quasiconvexity for f. The case 1 2 by a duality technique. |
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