Article - postprint
We prove that nonnegative solutions to a semilinear Dirichlet problem in a ball are positive, and hence radially symmetric. In particular, this answers a question in  where positive solutions were proven to be radially symmetric. In section 4 we provide a sufficient condition on the geometry of the domain which ensures that nonnegative solutions are positive in the interior.
© 1989 Marcel Dekker
Castro, Alfonso and R. Shivaji. “Non-negative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric,” Comm. in Partial Differential Equations, Vol. 14, No. 8-9, (1989), pp. 1091-1100.