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Resumen:
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Let ??R N be a bounded smooth domain, f,g?C 1 (R) , ? 1 ,? 2 ?C 2 (??) , b,c?C 2 (R) nondecreasing, ?,?:R?2 R maximal monotone such that 0??(0)??(0) and consider the weakly coupled elliptic system (?) ?u??(u)f(v) , ??v??(u)g(v) on ? with Dirichlet-boundary conditions u=? 1 , v=? 2 on ?? , or with the nonlinear boundary conditions ?u/?n+b(u)=? 1 , ?v/?n+c(v)=? 2 on ?? . Systems of this type arise in several applications, in particular as models for certain chemical reactions; here one typically has ?(u)=?(u)=|u| q sgnu , where q?0 is the order of the reaction. Assuming 0?m 1 ?f(s) , 0?g(s)?m 2 and ?(s)????(s) on R , the authors construct pairs of bounded sub/supersolutions of (?) and then prove, by a standard application of Schauder's theorem, existence of a solution (u,v) of (?) with either boundary condition satisfying u,v?W 1,p (?) for each p?[1,?) .
The second part of the paper is devoted to existence of a so-called "dead core'' for u , i.e., the set ? 0 =u ?1 (0) is of positive Lebesgue measure. For ?(u)=? 2 |u| q sgnu it is shown that a dead core only exists if 0?q
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