## Regularity of Weak Solutions of Semilinear Elliptic Differential Equations

J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 2, Page 357--363.

Uchida, Motoo
Regularity of Weak Solutions of Semilinear Elliptic Differential Equations
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 $p$.