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Eurasian Mathematical Journal, 2011, Volume 2, Number 2, Pages 129–133
(Mi emj56)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 26.05.2011
Citation:
B. N. Biyarov, “About the spectrum of the Laplace operator”, Eurasian Math. J., 2:2 (2011), 129–133
Linking options:
https://www.mathnet.ru/eng/emj56 https://www.mathnet.ru/eng/emj/v2/i2/p129
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Abstract page: | 338 | Full-text PDF : | 153 | References: | 70 |
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