# zbMATH — the first resource for mathematics

Nonlinear elliptic systems with measure data in low dimension. (English) Zbl 1236.35194
From the text: We consider the Dirichlet problem \begin{aligned} - \text{div}(A(x, Du(x))) = \mu \qquad \text{in }\Omega \\ u = 0 \qquad \text{on }\partial \Omega\end{aligned} where $$u: \Omega \subset \mathbb R^n \to \mathbb R^N$$, $$A$$ is an elliptic operator and $$\mu$$ is a measure on $$\mathbb R^n$$ with values into $$\mathbb R^n$$; thus the equation above is a system of $$N$$ elliptic equations. We prove existence of solutions in dimensions two and three.

##### MSC:
 35R06 PDEs with measure 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35J47 Second-order elliptic systems