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

Authors
Publisher
Universidad Autonoma de Madrid
Publication Date
Keywords
  • Mat/05 Analisi Matematica
Disciplines
  • Mathematics

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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