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Liouville theorems for elliptic inequalities and applications

Published online by Cambridge University Press:  14 November 2011

Isabeau Birindelli  and
Enzo Mitidieri
Isabeau Birindelli
Affiliation:
Dipartimento di Matematica, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 5, 00185 Rome, Italy
Enzo Mitidieri
Affiliation:
Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Piazzale Europa 1, 34100 Trieste, Italy
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Extract

In this paper we prove nonexistence of positive C2 solutions for systems of semilinear elliptic inequalities, for polyharmonic semilinear inequalities in cones and, under better conditions on the nonlinearity, for bounded positive solutions of elliptic semilinear equations in half spaces. Using a blow-up argument, these results allow us to prove a-priori bounds for a class of semilinear elliptic systems of equations in bounded domains.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1217 - 1247
Copyright
Copyright © Royal Society of Edinburgh 1998

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