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 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.