Geodesic
Partial regularity of solutions of quasilinear elliptic systems with nonsmooth condition on the~conormal derivative
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 215-230

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Partial regularity of a generalized solution $u\colon\Omega\subset\mathbb R^n\to\mathbb R^N$, $n>2$, $N>1$, of a quasilinear elliptic system is proved under a nonsmooth condition on the conormal derivative. The singular set $\Sigma\subset\overline\Omega$ is described; it is proved that for some $p>2$ the Hausdorff dimension of $\Sigma$ is equal to $n-p$. In the proof essential use is made of a theorem proved earlier by the author on reverse inequalities with surface integrals. 
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     author = {A. A. Arkhipova},
     title = {Partial regularity of solutions of quasilinear elliptic systems with nonsmooth condition on the~conormal derivative},
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     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_1_a13/}
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A. A. Arkhipova. Partial regularity of solutions of quasilinear elliptic systems with nonsmooth condition on the~conormal derivative. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 215-230. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a13/