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We give two-sided estimates for positive solutions of the superlinear
elliptic problem 
$-\unicode[STIX]{x1D6E5}u=a(x)|u|^{p-1}u$ with zero Dirichlet boundary condition in a bounded
Lipschitz domain. Our result improves the well-known a priori
$L^{\infty }$-estimate and provides information about the boundary decay
rate of solutions.
