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Zeitschrift für Analysis und ihre Anwendungen


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Volume 9, Issue 6, 1990, pp. 535–544
DOI: 10.4171/ZAA/422

Published online: 1990-12-31

On the Interior Regularity of Weak Solutions to Nonlinear Elliptic Systems of Second Order

Josef Daněček[1]

(1) Technical University of Brno, Czech Republic

The interior $C^{1, \alpha}$-regularity for a weak solution (with gradient in the BMO-space) of a non-linear second order elliptic system is investigated. The positive answer is obtained on the assumption that the elliptic system satisfy the generalized Liouville condition considered in the BMO-space instead of the usually used $L^{\infty}$-space. Finally it is proved that the Liouville condition holds in the case of $\mathbb R^2$.

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Daněček Josef: On the Interior Regularity of Weak Solutions to Nonlinear Elliptic Systems of Second Order. Z. Anal. Anwend. 9 (1990), 535-544. doi: 10.4171/ZAA/422