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Quaternionic Monge-Ampère equations. (English) Zbl 1058.32028
Das Hauptergebnis dieser Arbeit ist der Satz über die Existenz der eindeutigen Lösung des Dirichletschen Problems für die quaternionische Gleichung von Monge-Ampère in der Form \[ \text{det}\Biggl({\partial^2 u\over\partial q_i\partial\overline q_j}\Biggr)= f,\quad\text{in }\Omega \] in einem quaternionischen, streng pseudokonvexen Gebiet \(\Omega\subset\mathbb H^n\).

MSC:
32W20 Complex Monge-Ampère operators
15B33 Matrices over special rings (quaternions, finite fields, etc.)
35J60 Nonlinear elliptic equations
32U05 Plurisubharmonic functions and generalizations
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