Geodesic
On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations
Denisov, Vasily1 ; Muravnik, Andrey2
1 Moscow State University, Faculty of Computational Mathematics and Cybernetics, Leninskie gory, Moscow 119899, Russia
2 Department of Differential Equations, Moscow State Aviation Institute, Volokolamskoe shosse 4, Moscow, A-80, GSP-3, 125993, Russia
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 88-93 Cet article a éte moissonné depuis la source American Mathematical Society

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We study the Dirichlet problem in half-space for the equation ${\Delta u+g(u)|\nabla u|^2=0,}$ 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.
DOI : 10.1090/S1079-6762-03-00115-X

Denisov, Vasily 1 ; Muravnik, Andrey 2

1 Moscow State University, Faculty of Computational Mathematics and Cybernetics, Leninskie gory, Moscow 119899, Russia
2 Department of Differential Equations, Moscow State Aviation Institute, Volokolamskoe shosse 4, Moscow, A-80, GSP-3, 125993, Russia 
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Denisov, Vasily; Muravnik, Andrey. On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 88-93. doi: 10.1090/S1079-6762-03-00115-X

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