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

Gladiali, Francesca Maria and Damascelli, Lucio (2004) Some nonexistence results for positive solutions of elliptic equations in unbounded domains. Revista Matemática Iberoamericana, Vol. 20 (1), p. 67-86. ISSN 0213-2230. Article.

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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.

Item Type:Article
ID Code:4744
Status:Published
Refereed:Yes
Uncontrolled Keywords:Liouville theorems, Kelvin transform, maximum principle, moving plane
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 03 Istituti > Matematica e fisica
Publisher:Universidad Autonoma de Madrid
ISSN:0213-2230
Deposited On:29 Oct 2010 13:15

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