On the existence of the biharmonic Green kernels and the the adjoint   biharmonic functions
  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. 
Abderrahim Aslimani, Imad El Ghazi, Mohamed El Kadiri, Sabah Haddad
math.AP