Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 8 (2002), No. 2, Page 357-363
We consider elliptic systems of semilinear differential equations with nonlinearity of polynomial growth. We then prove that any locally $p$-integrable weak solution is smooth if $p\gg1$. We give a lower bound, optimal in the general setting, of the exponent $p$.