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Martin boundary associated with a system of PDE. (English) Zbl 1132.31005

Summary: In this paper, we study the Martin boundary associated with a harmonic structure given by a coupled partial differential equations system. We give an integral representation for non negative harmonic functions of this structure. In particular, we obtain such results for biharmonic functions (i.e.\(\triangle ^{2}\varphi =0\)) and for non negative solutions of the equation \(\triangle ^{2}\varphi = \varphi \).

MSC:

31C35 Martin boundary theory
31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
60J50 Boundary theory for Markov processes
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