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On the existence of the biharmonic Green kernels and the adjoint biharmonic functions

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Abstract

We study the existence and the regularity of the biharmonic Green kernel in a Brelot biharmonic space whose associated harmonic spaces have Green kernels. We show by some examples that this kernel does not always exist. We then introduce and study the adjoint of the given biharmonic space. This study was initiated by Smyrnelis, however, it seems that several results were incomplete and we clarify them here.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, P.B. 1014, Rabat, Morocco

    Abderrahim Aslimani, Imad El Ghazi & Mohamed El Kadiri

  2. CRMEF, Rabat-Akkari, Morocco

    Sabah Haddad

Authors
  1. Abderrahim Aslimani
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  2. Imad El Ghazi
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  3. Mohamed El Kadiri
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  4. Sabah Haddad
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Correspondence to Mohamed El Kadiri.

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Aslimani, A., El Ghazi, I., El Kadiri, M. et al. On the existence of the biharmonic Green kernels and the adjoint biharmonic functions. Ann Univ Ferrara 64, 25–46 (2018). https://doi.org/10.1007/s11565-017-0289-8

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  • DOI: https://doi.org/10.1007/s11565-017-0289-8

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