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On the existence of weak solutions for a class of elliptic partial differential systems. (English) Zbl 1219.35088
Summary: We obtain the existence of weak solutions for \[ \sum_{\alpha =1}^{n}\frac{\partial }{\partial x^{\alpha }} A_{\alpha }^{i}\left( x,u,Du\right) =B^{i}\left( x,u,Du\right),~ x\in\Omega,~ i=1,\dots ,N. \] in a Orlicz-Sobolev space. This generalizes the result of E. Acerbi and N. Fusco [Arch. Ration. Mech. Anal. 86, 125–145 (1984; Zbl 0565.49010)] by means of Orlicz space theory.

35J56 Boundary value problems for first-order elliptic systems
35J50 Variational methods for elliptic systems
35J60 Nonlinear elliptic equations
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