We prove some Liouville type theorems for positive solutions of semilinear elliptic equations in the whole space R-N, N greater than or equal to 3, and in the half space 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.
Damascelli, L., Gladiali, P. (2004). Some nonexistence results for positive solutions of elliptic equations in unbounded domains. REVISTA MATEMATICA IBEROAMERICANA, 20(1), 67-86.
Some nonexistence results for positive solutions of elliptic equations in unbounded domains
DAMASCELLI, LUCIO;
2004-01-01
Abstract
We prove some Liouville type theorems for positive solutions of semilinear elliptic equations in the whole space R-N, N greater than or equal to 3, and in the half space 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.File in questo prodotto:
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