Symmetric Harmonic Sheaves Possessing Bipotentials

Let be the family of sheaves H of continuous functions on a Brelot harmonic space with a countable base such that locally the Dirichlet problem with respect to H is solvable, H satisfies Harnack inequalities and also H has a symmetry property. Defining the notions of H-biharmonic functions, H-biharmonic Green functions, H-bipotentials, H-biharmonic extensions, etc. we study the interrelation between them and exhibit various classifications of the family of sheaves.