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Short communications

About the spectrum of the Laplace operator

B. N. Biyarov

Faculty of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan

Abstract: The famous French scientist J. Hadamard constructed the well-known example illustrating the incorrectness of the Cauchy problem for the Laplace equation. Since then, the question arises whether there exists a Volterra problem for the Laplace equation. In this paper we prove a theorem for a wide class of correct restrictions of the maximal operator $\widehat L$ and the correct extensions of the minimal operator $L_0$, generated by the Laplace operator, which are not Volterra problems.

Keywords and phrases: Laplace operator, Volterra operator, correct restrictions of the maximal operator, correct extensions of the minimal operator.

MSC: 35P05, 58J50

Received: 26.05.2011

Language: English

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