caa a22 4500 605496110 CHVBK 20210128100534.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10231-014-0441-3 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0441-3 A quasilinear elliptic system with natural growth terms [Elektronische Daten] [Lucio Boccardo, Luigi Orsina, Jean-Pierre Puel] In this paper, we prove existence of solutions for an elliptic system of the type $$\begin{aligned} {\left\{ \begin{array}{ll} -\mathrm{div}(a(x,z) \nabla u) = f, &{}\quad \text{ in } \varOmega \text{; } \\ -\mathrm{div}(b(x) \nabla z)+ h(x,z)|\nabla u|^2 = g, &{}\quad \text{ in } \varOmega \text{; } \\ \,u = 0 = z, &{}\quad \text{ on } \partial \varOmega \text{, } \end{array}\right. } \end{aligned}$$ - div ( a ( x , z ) ∇ u ) = f , in Ω ; - div ( b ( x ) ∇ z ) + h ( x , z ) | ∇ u | 2 = g , in Ω ; u = 0 = z , on ∂ Ω , under various assumptions on the functions $$a(x,s)$$ a ( x , s ) and $$h(x,s)$$ h ( x , s ) , and on the data $$f$$ f and $$g$$ g (in Lebesgue spaces). Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Nonlinear elliptic systems nationallicence Quasilinear quadratic elliptic equations nationallicence Existence and nonexistence of solutions nationallicence Boccardo Lucio Dipartimento di Matematica, "Sapienza” Università di Roma, P.le A. Moro 2, 00185, Rome, Italy aut Orsina Luigi Dipartimento di Matematica, "Sapienza” Università di Roma, P.le A. Moro 2, 00185, Rome, Italy aut Puel Jean-Pierre Laboratoire de Mathématiques de Versailles, Université de Versailles St Quentin, 45 Avenue des Etats Unis, 78035, Versailles Cedex, France aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1733-1750 0373-3114 194:6<1733 2015 194 10231 https://doi.org/10.1007/s10231-014-0441-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0441-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boccardo Lucio Dipartimento di Matematica, "Sapienza” Università di Roma, P.le A. Moro 2, 00185, Rome, Italy aut NATIONALLICENCE 700 1- Orsina Luigi Dipartimento di Matematica, "Sapienza” Università di Roma, P.le A. Moro 2, 00185, Rome, Italy aut NATIONALLICENCE 700 1- Puel Jean-Pierre Laboratoire de Mathématiques de Versailles, Université de Versailles St Quentin, 45 Avenue des Etats Unis, 78035, Versailles Cedex, France aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1733-1750 0373-3114 194:6<1733 2015 194 10231