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We consider the semilinear elliptic equation — Au = /(«), x € f2, subject to zero Dirichlet boundary conditions, where f2 C Rn is a bounded domain with smooth boundary and the nonlinearity / assumes both positive and negative values. Under the assumption that O satisfies certain symme- try conditions we establish two results providing lower bounds on the C°(Q) norm of positive solutions. The bounds derived are the same one obtains in dimension n — 1.

A priori bounds for positive solutions of a semilinear elliptic equation