# zbMATH — the first resource for mathematics

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)