Abstract. We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain of R N (N 2), ( u + u q = 0 in u = on @ where 1 < q < (N + 1 ) =(N ; 1) and is a Radon measure on @ . We give a priori estimates and existence results. They lie on the study of the superharmonic functions in some weighted Marcinkiewicz spaces.
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