Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term

A. Dall'Aglio; D. Giachetti; C. Leone; S. Segura de León

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We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is $\{\begin{matrix} - div ((1 + {|u|}^{r}) \nabla u) + {|u|}^{m - 2} u {|\nabla u|}^{2} = f & in Ω \\ u = 0 & su \partial Ω . \end{matrix}$