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
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Abstract:
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 $p$.

Keywords: Weak solution, semilinear elliptic differential equation

Mathematics Subject Classification (2000): 35B65, 35D10, 35J60
Mathematical Reviews Number: MR1837169

Received: 2000-12-05