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Subject: Dirichlet problem

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Now showing 1 - 5 of 5
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    Conference Object
    Citation - Scopus: 17
    Dirichlet Problems for the Generalized N-Poisson Equation
    (Springer International Publishing, 2010) Aksoy,Ü.; Çelebi,A.O.
    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. © 2009 Birkhäuser Verlag Basel/Switzerland.
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    Article
    Dirichlet-Type Problems for n-poisson Equation in Clifford Analysis
    (Taylor & Francis Ltd, 2022) Aksoy, Umit; Celebi, A. Okay
    Iterated Dirichlet problem, also called as Riquier or Navier problem, and polyharmonic Dirichlet problem are studied for n-Poisson equation in Clifford analysis using iterated polyharmonic Green function and polyharmonic Green-Almansi type function appropriate for the boundary conditions of the problems.
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    Book Part
    Dirichlet Problem for Inhomogeneous Biharmonic Equation in Clifford Analysis
    (Springer Science and Business Media Deutschland GmbH, 2022) Aksoy,Ü.; Çelebi,A.O.
    An integral representation formula in terms of the bi-Laplacian operator is obtained and Dirichlet problem for the bi-Poisson equation is solved in Clifford analysis. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
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    Conference Object
    Citation - WoS: 12
    Dirichlet Problems for the Generalized n-poisson Equation
    (Birkhauser verlag Ag, 2010) Aksoy, U.; Celebi, A. O.
    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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    Article
    Citation - WoS: 6
    Citation - Scopus: 9
    Dirichlet Problem for a Generalized Inhomogeneous Polyharmonic Equation in an Annular Domain
    (Taylor & Francis Ltd, 2012) Aksoy, U.; Celebi, A. O.
    In this article, we investigate the solvability of the Dirichlet problems in ring domains for elliptic linear complex partial differential equations having polyharmonic operators as main parts. First, we give higher order Green functions as fundamental solutions of the homogeneous problems using the iteration of harmonic Green functions for ring domains. Second, we introduce some classes of operators related to Dirichlet problems together with their basic properties. Next, we transform the original problems into equivalent singular integral equations. Finally, solvability of the problems is discussed by defining the adjoint problems and using Fredholm alternative.