On the Fragmen–Lindelof theorems for quasilinear elliptic equations of the second order - Kurta , V. V. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
Analogues are formulated of the well–known, in the theory of analytic functions, Phragmen–Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form $div(| abla u|^{α–2} abla u)=f(x,u, abla u)$, where $f(x,u, abla u)$ is a function locally bounded in ${\mathbb R}^{2n+1}$. $f(x,u, abla u) = 0$, $u f (x,u, abla u) ≥ c| u |^{1+q}(1+| abla u|)^{γ}$, $α > 1$, $c > 0$, $q > 0$, $γ$ is an arbitrary real number, and $n≥ 2$. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.