Geodesic
On the Spectrum of the Robin Problem in a Domain with a Peak
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 93-96

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A formally self-adjoint Robin–Laplace problem in a peak-shaped domain is considered. The associated quadratic form is not semi-bounded, which is proved to lead to a pathological structure of the spectrum of the corresponding operator. Namely, the residual spectrum of the operator itself and the point spectrum of its adjoint cover the whole complex plane. The operator is not self-adjoint, and the (discrete) spectrum of any of its self-adjoint extensions is not semi-bounded.
Keywords: Robin condition, third boundary value problem, peak, spectrum, asymptotics, self-adjoint extension.
Mots-clés : cusp 
S. A. Nazarov; Ya. Taskinen. On the Spectrum of the Robin Problem in a Domain with a Peak. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 93-96. http://geodesic.mathdoc.fr/item/FAA_2011_45_1_a9/
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