Some identities of Green's function for the polyharmonic operator with the Navier boundary conditions and its applications

Authors

  • Futoshi Takahashi

    Corresponding author
    1. Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
    • Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan. Phone: +81 (0)6 6605 2508, Fax: +81 (0)6 6605 2515
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Abstract

We prove several integral identities for Green's function of the polyharmonic operator equation image, under the Navier boundary conditions. As an application, we prove the nondegeneracy of the critical point of the Robin function associated to the Green function on some symmetric domains.

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