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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 5, Pages 977–1010 (Mi izv2572)  

This article is cited in 17 scientific papers (total in 17 papers)

Isolation of singularities of the Green's function

Yu. P. Krasovskii


Abstract: A method is given for constructing the Green's function for general boundary-value problems for elliptic equations. Pointwise estimates are proved for the Green's function in a closed region. A representation of an arbitrary solution of the boundary-value problem is derived, which permits the explicit construction of the irregular part of the solution if the latter contains singularities.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:5, 935–966

Bibliographic databases:

UDC: 517.9
MSC: 35A20, 35J25
Received: 05.03.1966

Citation: Yu. P. Krasovskii, “Isolation of singularities of the Green's function”, Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967), 977–1010; Math. USSR-Izv., 1:5 (1967), 935–966

Citation in format AMSBIB
\Bibitem{Kra67}
\by Yu.~P.~Krasovskii
\paper Isolation of singularities of the Green's function
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 5
\pages 977--1010
\mathnet{http://mi.mathnet.ru/izv2572}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=223740}
\zmath{https://zbmath.org/?q=an:0153.42701|0174.15703}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 5
\pages 935--966
\crossref{https://doi.org/10.1070/IM1967v001n05ABEH000594}


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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. Yu. P. Krasovskii, “Green function properties and generalized solutions of elliptic boundary value problems”, Math. USSR-Izv., 3:1 (1969), 105–130  mathnet  crossref  mathscinet  zmath
    2. Yu. P. Krasovskii, “Differential properties of solutions of elliptic boundary-value problems with power singularities on the right-hand sides”, Math. USSR-Izv., 5:1 (1971), 211–219  mathnet  crossref  mathscinet  zmath
    3. S. D. Ivasishen, “Green's matrices of boundary value problems for Petrovskii parabolic systems of general form. I”, Math. USSR-Sb., 42:1 (1982), 93–144  mathnet  crossref  mathscinet  zmath
    4. S. D. Ivasishen, “Green's matrices of boundary value problems for Petrovskii parabolic systems of general form. II”, Math. USSR-Sb., 42:4 (1982), 461–498  mathnet  crossref  mathscinet  zmath
    5. C. I. Goldstein, L. R. Scott, “Optimal maximum norm error estimates for some finite element methods for treating the Dirichlet problem”, Calcolo, 20:1 (1983), 1  crossref
    6. Wei-Shih Yang, “The Simon-Lieb inequality for the φ4-theory in two dimensions”, Journal of Functional Analysis, 77:1 (1988), 139  crossref
    7. Wen-ming He, “A new superconvergence and extrapolation for second order triangular element”, Applied Mathematics and Computation, 174:1 (2006), 300  crossref
    8. Wen-ming He, Jun-zhi Cui, “A new approximate method for second order elliptic problems with rapidly oscillating coefficients based on the method of multiscale asymptotic expansions”, Journal of Mathematical Analysis and Applications, 335:1 (2007), 657  crossref
    9. Wen-ming He, “Error estimates of finite element method about elliptic problems with singular righthand side”, Applied Mathematics and Computation, 188:1 (2007), 824  crossref
    10. Wen-ming He, “High effective finite element algorithm for elliptic partial differential equation”, Applied Mathematics and Computation, 187:2 (2007), 1567  crossref
    11. Wen-Ming He, Wei-Qiu Chen, Qi-Ding Zhu, “Local superconvergence of the derivative for tensor-product block FEM”, Numer Methods Partial Differential Eq, 2010, n/a  crossref
    12. Marius Ghergu, “A biharmonic equation with singular nonlinearity”, Proceedings of the Edinburgh Mathematical Society, 2011, 1  crossref
    13. Antti V. Vähäkangas, “On Regularity and Extension of Green’s Operator on Bounded Smooth Domains”, Potential Anal, 2011  crossref
    14. Wen-ming He, Xiao-fei Guan, Jun-zhi Cui, “The local superconvergence of the trilinear element for the three-dimensional Poisson problem”, Journal of Mathematical Analysis and Applications, 2011  crossref
    15. Wen-ming He, Jun-Zhi Cui, Qi-ding Zhu, Zhong-liang Wen, “The local superconvergence of the linear finite element method for the Poisson problem”, Numer. Methods Partial Differential Eq, 2013, n/a  crossref
    16. Wen-Ming He, Jun-Zhi Cui, Qi-Ding Zhu, “The local superconvergence of the quadratic triangular element for the Poisson problem in a polygonal domain”, Numer. Methods Partial Differential Eq, 2014, n/a  crossref
    17. Xiaofei Guan, Mingxia Li, Wenming He, Zhengwu Jiang, “Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients”, centr.eur.j.math, 12:11 (2014), 1733  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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