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A generic property of the resonance set of an elliptic operator with respect to the domain*

Published online by Cambridge University Press:  14 November 2011

Angela Pistoia
Angela Pistoia
Affiliation:
Dipartimento di Matematica Applicata ‘U Dini’, Facoltá di Ingegneria, via Bonanno 25, 56100 Pisa, Italy email: [email protected]
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Extract

The set of points (α, β) ∈ℝ2 for which the problem − δu = αu+ − βu− in Ω, u = 0 on ∂Ω(u+ = max {u, o} and u− = min {−u, 0}) has nontrivial solutions is important for the study of certain nonlinear problems. It is shown that for ‘most’ bounded domains Ω in ℝn, such a set is locally the union of a finite number of curves.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 6 , 1997 , pp. 1301 - 1310
Copyright
Copyright © Royal Society of Edinburgh 1997

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