Regularity of Weak Solutions of Semilinear Elliptic Differential Equations
Vol. 8 (2001), No. 2, Page 357--363.
Uchida, Motoo
Regularity of Weak Solutions of Semilinear Elliptic Differential Equations
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
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
