Abstract
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(|∇U|α−2∇u)=f(x, u, ∇u), where f(x, u, ∇u) is a function locally bounded in ℝ2n+1. f(x, 0, ∇u)=0, uf(x, u, ∇u) ≥ c¦u¦1+q(1+ ¦∇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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.
The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions.
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Kurta, V.V. Phragmén-Lindelöf theorems for second-order quasilinear elliptic equations. Ukr Math J 44, 1262–1268 (1992). https://doi.org/10.1007/BF01057683
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DOI: https://doi.org/10.1007/BF01057683