Regularity results for positive solutions of a semilinear elliptic system

Let, N≧3 be an open set. In this paper we study weak positive solutions of the following semilinear systemwhere p≧1, q≧1, with pq>1, and u∈Lq(Ω), v∈Lp(Ω), and we give in particular some regularity results. Furthermore, we give some applications to the biharmonic equation.