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 | References | Similar Articles | Additional Information

Abstract: We study the Dirichlet problem in half-space for the equation where 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 where 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

DOI:
http://dx.doi.org/10.1090/S1079-6762-03-00115-X

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