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
DOI:
https://doi.org/10.1090/S1079-6762-03-00115-X
Published electronically:
September 29, 2003
MathSciNet review:
2029469
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Abstract: 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.
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Additional Information
Vasily Denisov
Affiliation:
Moscow State University, Faculty of Computational Mathematics and Cybernetics, Leninskie gory, Moscow 119899, Russia
Email:
V.Denisov@g23.relcom.ru
Andrey Muravnik
Affiliation:
Department of Differential Equations, Moscow State Aviation Institute, Volokolamskoe shosse 4, Moscow, A-80, GSP-3, 125993, Russia
Email:
abm@mailru.com
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
