B. E. Kanguzhin, A. A. Anijarov, “Well-Posed Problems for the Laplace Operator in a Punctured Disk”, Mat. Zametki, 89:6 (2011), 856–867; Math. Notes, 89:6 (2011), 819

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Matematicheskie Zametki, 2011, Volume 89, Issue 6, Pages 856–867
DOI: https://doi.org/10.4213/mzm8767 (Mi mzm8767)

This article is cited in 41 scientific papers (total in 41 papers)

Well-Posed Problems for the Laplace Operator in a Punctured Disk

B. E. Kanguzhin^a, A. A. Anijarov^b

^a Al-Farabi Kazakh National University
^b Semipalatinsk State Pedagogical Institute

Full-text PDF (463 kB) Citations (41)

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DOI: https://doi.org/10.4213/mzm8767

Abstract: We give a complete description of well-posed solvable boundary-value problems for the Laplace operator in the disk and in the punctured disk. We present formulas for resolvents of well-posed problems for the Laplace operator in the disk.

Keywords: Laplace operator, well-posed solvable boundary-value problem, punctured disk, nonhomogeneous Laplace equation, Dirichlet boundary condition, Green function, Dirac function.

Received: 03.01.2010
Revised: 01.09.2010

English version:
Mathematical Notes, 2011, Volume 89, Issue 6, Pages 819–829
DOI: https://doi.org/10.1134/S0001434611050233

Bibliographic databases:

Document Type: Article

UDC: 517.95

Language: Russian

Citation: B. E. Kanguzhin, A. A. Anijarov, “Well-Posed Problems for the Laplace Operator in a Punctured Disk”, Mat. Zametki, 89:6 (2011), 856–867; Math. Notes, 89:6 (2011), 819–829

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm8767

https://doi.org/10.4213/mzm8767

https://www.mathnet.ru/eng/mzm/v89/i6/p856

This publication is cited in the following 41 articles:

Makhmud Sadybekov, Batirkhan Turmetov, Trends in Mathematics, 1, Extended Abstracts MWCAPDE 2023, 2024, 187
Karlygash Dosmagulova, Baltabek Kanguzhin, Trends in Mathematics, 5, Women in Analysis and PDE, 2024, 145
Andrés F. Guerra Riaño, Péter L. Várkonyi, “Structural form finding using the Stress Density Method: Well-posedness and convergence of numerical solutions”, International Journal of Solids and Structures, 2024, 113156
Baltabek KANGUZHİN, Karlygash DOSMAGULOVA, “Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere”, Advances in the Theory of Nonlinear Analysis and its Application, 7:2 (2023), 428
Kanguzhin B.E., Tulenov K.S., “Correctness of the Definition of the Laplace Operator With Delta-Like Potentials”, Complex Var. Elliptic Equ., 67:4 (2022), 898–920
Baltabek Kanguzhin, Yerkebulan Akanbay, Zhalgas Kaiyrbek, “On the Uniqueness of the Recovery of the Domain of the Perturbed Laplace Operator”, Lobachevskii J Math, 43:6 (2022), 1532
Kanguzhin B., Fazullin Z., “On the Localization of the Spectrum of Some Perturbations of a Two-Dimensional Harmonic Oscillator”, Complex Var. Elliptic Equ., 66:6-7 (2021), 1194–1208
G. E. Abduakhitova, B. E. Kanguzhin, “Korrektnoe opredelenie ellipticheskikh operatorov vtorogo poryadka s tochechnymi vzaimodeistviyami i ikh rezolventy”, Matem. tr., 23:1 (2020), 3–15
Kanguzhin B.E., Tulenov K.S., “Singular Perturbations of Laplace Operator and Their Resolvents”, Complex Var. Elliptic Equ., 65:9 (2020), 1433–1444
Fazullin Z.Yu. Madibaiuly Zh. Yermekkyzy L., “Control of Vibrations of Elastically Fixed Objects Using Analysis of Eigenfrequencies”, Int. J. Math. Phys.-Kazakhstan, 11:2 (2020), 27–31
G. E. Abduakhitova, B. E. Kanguzhin, “The Correct Definition of Second-Order Elliptic Operators with Point Interactions and their Resolvents”, Sib. Adv. Math., 30:3 (2020), 153
B. Kanguzhin, L. Zhapsarbaeva, Zh. Madibaiuly, “Lagrange formula for differential operators and self-adjoint restrictions of the maximal operator on a tree”, Eurasian Math. J., 10:1 (2019), 16–29
Bekbolat B., Kanguzhin B., Tokmagambetov N., “To the Question of a Multipoint Mixed Boundary Value Problem For a Wave Equation”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 4:326 (2019), 76–82
Bekbolat B. Nurakhmetov D.B. Tokmagambetov N. Rasa G.H.A., “On the Minimality of Systems of Root Functions of the Laplace Operator in the Punctured Domain”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 4:326 (2019), 92–109
Kanguzhin B.E., “Changes in a Finite Part of the Spectrum of the Laplace Operator Under Delta-Like Perturbations”, Differ. Equ., 55:10 (2019), 1328–1335
Nalzhupbayeva G., “Remark on the Eigenvalues of the M-Laplacian in a Punctured Domain”, Complex Anal. Oper. Theory, 12:3 (2018), 599–606
Nalzhupbayeva G., “Spectral Properties of One Elliptic Operator in a Punctured Domain”, AIP Conference Proceedings, 1997, ed. Ashyralyev A. Lukashov A. Sadybekov M., Amer Inst Physics, 2018, UNSP 020083-1
B. E. Kanguzhin, D. Dauitbek, “A maximum of the first eigenvalue of semibounded differential operator with a parameter”, Russian Math. (Iz. VUZ), 61:2 (2017), 10–16
Koshkarbayev N., Kanguzhin B., “Lagrange Formula For Differential Operators on a Tree-Graph and the Resolvents of Well-Posed Restrictions of Operator”, International Conference Functional Analysis in Interdisciplinary Applications (FAIA2017), AIP Conference Proceedings, 1880, eds. Kalmenov T., Sadybekov M., Amer Inst Physics, 2017, UNSP 050017
Nalzhupbayeva G., “Formulas For the Eigenvalues of the Iterated Laplacian With Singular Potentials”, International Conference Functional Analysis in Interdisciplinary Applications (FAIA2017), AIP Conference Proceedings, 1880, ed. Kalmenov T. Sadybekov M., Amer Inst Physics, 2017, UNSP 050005

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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