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On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations

Authors: Vasily Denisov and Andrey Muravnik
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 88-93
MSC (2000): Primary 35J25; Secondary 35B40, 35J60
Published electronically: September 29, 2003
MathSciNet review: 2029469
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Abstract: We study the Dirichlet problem in half-space for the equation $\nobreak{\Delta u+g(u)\vert\nabla u\vert^2=0,}$ where $g$ is continuous or has a power singularity (in the latter case positive solutions are considered). The results presented give necessary and sufficient conditions for the existence of (pointwise or uniform) limit of the solution as $y\to\infty,$ where $y$ denotes the spatial variable, orthogonal to the hyperplane of boundary-value data. These conditions are given in terms of integral means of the boundary-value function.

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Additional Information

Vasily Denisov
Affiliation: Moscow State University, Faculty of Computational Mathematics and Cybernetics, Leninskie gory, Moscow 119899, Russia

Andrey Muravnik
Affiliation: Department of Differential Equations, Moscow State Aviation Institute, Volokolamskoe shosse 4, Moscow, A-80, GSP-3, 125993, Russia

Keywords: Asymptotic behaviour of solutions, BKPZ-type non-linearities
Received by editor(s): March 6, 2002
Published electronically: September 29, 2003
Additional Notes: The second author was supported by INTAS, grant 00-136 and RFBR, grant 02-01-00312.
Communicated by: Michael E. Taylor
Article copyright: © Copyright 2003 American Mathematical Society