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March, 2004 Some nonexistence results for positive solutions of elliptic equations in unbounded domains
Lucio Damascelli, Francesca Gladiali
Rev. Mat. Iberoamericana 20(1): 67-86 (March, 2004).

Abstract

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.

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Lucio Damascelli. Francesca Gladiali. "Some nonexistence results for positive solutions of elliptic equations in unbounded domains." Rev. Mat. Iberoamericana 20 (1) 67 - 86, March, 2004.

Information

Published: March, 2004
First available in Project Euclid: 2 April 2004

zbMATH: 1330.35146
MathSciNet: MR2076772

Subjects:
Primary: 35B05 , 35B45 , 35B50

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

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.20 • No. 1 • March, 2004
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