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Non-linear elliptic systems involving measure data. (English) Zbl 0838.35133
This paper gives an existence theorem for the Dirichlet problem in a bounded smooth domain in \(\mathbb{R}^n\), for the system \(-\text{div}|\nabla u|^{p- 2}\nabla u= T\), where \(u\) is a vector, \(n\geq 3\) and \(p> 2- 1/n\). \(T\) is a Radon measure supported on a set of measure zero. The authors also announce results for more general measures. The proofs are very briefly outlined.

MSC:
35R05 PDEs with low regular coefficients and/or low regular data
35J60 Nonlinear elliptic equations
35J45 Systems of elliptic equations, general (MSC2000)
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