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Biharmonic Martin boundary and integral representation of biharmonic functions. (Frontière de Martin biharmonique et représentation intégrale des fonctions biharmoniques.) (French) Zbl 0998.31004
A suitable definition for the biharmonic Martin boundary allows an integral representation for non-negative biharmonic pairs of functions on a strong biharmonic space in the sense of E. Smyrnelis [Ann. Inst. Fourier 26, 35-98 (1975; Zbl 0295.31006)].
The Riquier problem with respect to this Martin boundary is solved, too.

MSC:
31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
31C35 Martin boundary theory
31D05 Axiomatic potential theory
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
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