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The pluriharmonic problem in a spherical domain of n for n3. (Italian) Zbl 0577.32017

The author presents a finite collection of explicit second order linear partial differential operators on the boundary bΩ of the unit ball Ω in n , such that the corresponding homogeneous system of PDE characterizes the boundary values of pluriharmonic functions on Ω, provided n3. The result has also a local version.

Similar results were found earlier by T. Audibert [C.R. Acad. Sci., Paris, Sér. A 284, 1029-1031 (1977; Zbl 0346.31004)] and M. Nacinovich [Complex analysis, Proc. Summer Sch., Trieste 1980, Lect. Notes Math. 950, 105-195 (1982; Zbl 0513.32029)].

Reviewer: R.M.Range
MSC:
32U05Plurisubharmonic functions and generalizations
31C10Pluriharmonic and plurisubharmonic functions
35G05General theory of linear higher-order PDE