B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov, “Laplace operator with <nobr>$\delta$</nobr>-like potentials”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 2,Pages <nobr>9

This article is cited in 24 papers

Laplace operator with $\delta$-like potentials

B. E. Kanguzhin^a, D. B. Nurakhmetov^a, N. E. Tokmagambetov^b

^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