We prove some Liouville type theorems for positive solutions
of semilinear elliptic equations in the whole space $\mathbb{R}^N$,
$N\geq 3$, and in the half space $\mathbb{R}^N_{+}$
with different boundary conditions, using the technique
based on the Kelvin transform and the Alexandrov-Serrin method
of moving hyperplanes. In particular we get new nonexistence
results for elliptic problems in half spaces satisfying mixed
(Dirichlet-Neumann) boundary conditions.
Publié le : 2004-03-14
Classification:
Liouville theorems,
Kelvin transform,
maximum principle,
moving plane,
35B05,
35B45,
35B50
@article{1080928420,
author = {Damascelli, Lucio and Gladiali, Francesca},
title = {Some nonexistence results for positive solutions of
elliptic equations in unbounded domains},
journal = {Rev. Mat. Iberoamericana},
volume = {20},
number = {1},
year = {2004},
pages = { 67-86},
language = {en},
url = {http://dml.mathdoc.fr/item/1080928420}
}
Damascelli, Lucio; Gladiali, Francesca. Some nonexistence results for positive solutions of
elliptic equations in unbounded domains. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp. 67-86. http://gdmltest.u-ga.fr/item/1080928420/