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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2014 Number 2, Pages 9–16 (Mi ivm8866)

This article is cited in 24 papers

Laplace operator with $\delta$-like potentials

B. E. Kanguzhina, D. B. Nurakhmetova, N. E. Tokmagambetovb

a Chair of Fundamental Mathematics, al-Farabi Kazakh National University, 71 al-Farabi Ave., Almaty, 500040 Republic of Kazakhstan
b Institute of Mathematics and Mathematical Modelling MES RK, 28 Shevchenko str., Almaty, 500012 Republic of Kazakhstan

Abstract: We study the Laplace operator in a punctured domain in a Hilbert space. We obtain an analog of the Green formula and a class of self-adjoint extensions of the Laplacian. We also investigate a certain class of well-posed problems.

Keywords: Laplace operator, punctured domain, analog of the Green formula, self-adjoint extension, well-posed problem.

UDC: 517.95

Received: 12.10.2012


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:2, 6–12

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