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Mat. Zametki, 2011, Volume 89, Issue 6, Pages 856–867 (Mi mz8767)  

This article is cited in 18 scientific papers (total in 18 papers)

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

B. E. Kanguzhina, A. A. Anijarovb

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

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

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

Full text: PDF file (463 kB)
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English version:
Mathematical Notes, 2011, 89:6, 819–829

Bibliographic databases:

UDC: 517.95
Received: 03.01.2010
Revised: 01.09.2010

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

    This publication is cited in the following articles:
    1. B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov, “Approksimativnye svoistva sistem kornevykh funktsii, porozhdaemye korrektno razreshimymi kraevymi zadachami dlya obyknovennykh differentsialnykh uravnenii vysshikh poryadkov”, Ufimsk. matem. zhurn., 3:3 (2011), 80–92  mathnet  zmath
    2. B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov, “Laplace operator with $\delta$-like potentials”, Russian Math. (Iz. VUZ), 58:2 (2014), 6–12  mathnet  crossref
    3. M. E. Akhymbek, D. B. Nurakhmetov, “Pervyi regulyarizovannyi sled operatora dvukratnogo differentsirovaniya na prokolotom otrezke”, Sib. elektron. matem. izv., 11 (2014), 626–633  mathnet
    4. Kanguzhin B.E., Tokmagambetov N.E., “a Regularized Trace Formula For a Well-Perturbed Laplace Operator”, Dokl. Math., 91:1 (2015), 1–4  crossref  mathscinet  zmath  isi  scopus
    5. Kanguzhin B.E., Tokmagambetov N.E., “On regularized trace formulas for a well-posed perturbation of the m-Laplace operator”, Differ. Equ., 51:12 (2015), 1583–1588  crossref  mathscinet  zmath  isi  elib  scopus
    6. Akhymbek M.E., Yessirkegenov N.A., Sadybekov M.A., “Renovation of the Fixing and Loading Factors of the Beam By the Spectral Data of Free Flexural Vibrations”, Advancements in Mathematical Sciences (Ams 2015), AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020058  crossref  isi  scopus
    7. Kanguzhin B., Tokmagambetov N., Bekbayev N., “The Green function and correctly solvable non–local boundary value problems for the polyharmonic equation in a punctured domain”, ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences (Antalya, Turkey, 5–7 November 2015), AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020101  crossref  isi  scopus
    8. Tokmagambetov N., Nalzhupbayeva G., “Operator perturbed Cauchy problem for the Gellerstedt equation”, ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences (Antalya, Turkey, 5–7 November 2015), AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020098  crossref  isi  scopus
    9. B. E. Kanguzhin, N. E. Tokmagambetov, “Resolvents of well-posed problems for finite-rank perturbations of the polyharmonic operator in a punctured domain”, Siberian Math. J., 57:2 (2016), 265–273  mathnet  crossref  crossref  mathscinet  isi  elib
    10. Medet Nursultanov, “Spectral Properties of the Schrödinger Operator with $\delta$-Distribution”, Math. Notes, 100:2 (2016), 263–275  mathnet  crossref  crossref  mathscinet  isi  elib
    11. Akhymbek M., Yessirkegenov N., “Renovation of Unknown Coefficients of Fixing and Loading By the Spectral Data”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conference Proceedings, 1789, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2016, UNSP 040003  crossref  isi  scopus
    12. Sarsenbi A.A., Zhumanova L.K., “First Regularized Trace of Integro-Differential Sturm-Liouville Operator on a Segment With Punctured Points At Generalized Conditions of Bonding in Deleted Points”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conference Proceedings, 1789, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2016, UNSP 040009  crossref  isi  scopus
    13. 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  mathnet  crossref  isi
    14. 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  crossref  isi  scopus
    15. 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  crossref  isi  scopus
    16. Nalzhupbayeva G., “Remark on the Eigenvalues of the M-Laplacian in a Punctured Domain”, Complex Anal. Oper. Theory, 12:3 (2018), 599–606  crossref  mathscinet  zmath  isi  scopus
    17. 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  crossref  isi  scopus
    18. 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  mathnet  crossref
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