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Dirichlet Problems for the Generalized n -Poisson Equation

BROWSE_DETAIL_CREATION_DATE: 25-06-2015

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BROWSE_DETAIL_TYPE: Article

BROWSE_DETAIL_PUBLISH_STATE: Published

BROWSE_DETAIL_FORMAT: No File

BROWSE_DETAIL_LANG: English

BROWSE_DETAIL_SUBJECTS: SCIENCE, Mathematics,

BROWSE_DETAIL_CREATORS: Aksoy, Ümit (Author), Çelebi, Okay (Author),

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Operator TheoryPartial Differential Equations



    BROWSE_DETAIL_TAB_ABSTRACT

    Polyharmonic hybrid Green functions, obtained by convoluting polyharmonic Green and Almansi Green functions, are taken as kernels to define a hierarchy of integral operators. They are used to investigate the solvability of some types of Dirichlet problems for linear complex partial differential equations with leading term as the polyharmonic operator.


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    BROWSE_DETAIL_TAB_REFERENCES[1]E. Almansi, Sull’integrazione dell’equazione differenziale Δ 2n u=0, Ann. Mat. (3) 2 (1899), 1–59.[2]Ü. Aksoy and A.O. Çelebi, Neumann problem for generalized n-Poisson equation, J. Math. Anal. Appl. 357 (2009), 438–446.MATHView ArticleMathSciNet[3]H. Begehr and T. Vaitekhovich, Iterated Dirichlet problem for the higher order Poisson equation, Le Matematiche XIII (2008), 139–154.MathSciNet[4]H. Begehr and T. Vaitekhovich, Green functions in complex plane domains, Uzbek Math. J. 4 (2008), 29–34.[5]H. Begehr, J. Du and Y. Wang, A Dirichlet problem for polyharmonic functions, Ann. Mat. Pure Appl. 187 (2008), 435–457.MATHView ArticleMathSciNet[6]H. Begehr, A particular polyharmonic Dirichlet problem, in: Complex Analysis, Potential Theory, Editors: T. Aliyev Azeroglu and T.M. Tamrazov, World Scientific, 2007, 84–115.[7]H. Begehr and E. Gaertner, A Dirichlet problem for the inhomogeneous polyharmonic equation in the upper half plane, Georg. Math. J. 14 (2007), 33–52.MATHMathSciNet[8]H. Begehr, T.N.H. Vu and Z. Zhang, Polyharmonic Dirichlet problems, Proc. Steklov Inst. Math. 255 (2006), 13–34.View ArticleMathSciNet[9]H. Begehr, Six biharmonic Dirichlet problems in complex analysis, in: Function Spaces in Complex and Clifford Analysis, Natl. Univ. Publ. Hanoi: Hanoi, 2008, 243–252.[10]H. Begehr, Biharmonic Green functions, Le Mathematiche, LXI (2006), 395–405.MathSciNet[11]H. Begehr, Hybrid Green functions and related boundary value problems, in Proc. 37th Annual Iranian Math. Conf., 2006, 275–278.[12]H. Begehr, Boundary value problems in complex analysis I, II, Boletin de la Asosiación Matemática Venezolana, XII (2005), 65–85, 217–250.[13]H. Begehr, Boundary value problems for the Bitsadze equation, Memoirs on differential equations and mathematical physics 33 (2004), 5–23.MATHMathSciNet[14]S.S. Kutateladze, Fundamentals of Functional Analysis, Kluwer Academic Publishers, 1996.[15]T. Vaitsiakhovich, Boundary Value Problems for Complex Partial Differential Equations in a Ring Domain, Ph.D. Thesis, Freie Universität Berlin, 2008.[16]I.N. Vekua, Generalized Analytic Functions, Pergamon Press, 1962.


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