Abstract <p>The Green’s function of the biharmonic Navier problem in the unit ball is investigated. In contrast to the form of the Green’s function previously obtained by the author, here we present a representation in which the singularity of the fundamental solution of the biharmonic equation is explicitly expressed. Then, based on the Green’s function, an integral representation of the solution of the Navier problem in the unit ball is presented. In conclusion, a representation of the solution of the Navier problem for the homogeneous biharmonic equation is obtained without explicit use of the Green’s function. An illustrative example is given.</p>

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Representation of the Green’s Function of the Biharmonic Navier Problem

  • V. Karachik

摘要

Abstract

The Green’s function of the biharmonic Navier problem in the unit ball is investigated. In contrast to the form of the Green’s function previously obtained by the author, here we present a representation in which the singularity of the fundamental solution of the biharmonic equation is explicitly expressed. Then, based on the Green’s function, an integral representation of the solution of the Navier problem in the unit ball is presented. In conclusion, a representation of the solution of the Navier problem for the homogeneous biharmonic equation is obtained without explicit use of the Green’s function. An illustrative example is given.