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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
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