Revista Matemática Iberoamericana


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Volume 20, Issue 1, 2004, pp. 67–86
DOI: 10.4171/RMI/380

Published online: 2004-04-30

Some nonexistence results for positive solutions of elliptic equations in unbounded domains

Lucio Damascelli[1] and Francesca Gladiali[2]

(1) Università di Roma 'Tor Vergata', Italy
(2) Università di Roma La Sapienza, Italy

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.

Keywords: Liouville theorems, Kelvin transform, maximum principle, moving plane

Damascelli Lucio, Gladiali Francesca: Some nonexistence results for positive solutions of elliptic equations in unbounded domains. Rev. Mat. Iberoam. 20 (2004), 67-86. doi: 10.4171/RMI/380