Vol. 12, No. 2, 2019

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On the maximal rank problem for the complex homogeneous Monge–Ampère equation

Julius Ross and David Witt Nyström

Vol. 12 (2019), No. 2, 493–503
DOI: 10.2140/apde.2019.12.493

We give examples of regular boundary data for the Dirichlet problem for the complex homogeneous Monge–Ampère equation over the unit disc, whose solution is completely degenerate on a nonempty open set and thus fails to have maximal rank.

32W20, 35J60, 31C10, 35J70
Mathematical Subject Classification 2010
Primary: 32W20, 58J32
Received: 8 December 2017
Revised: 6 April 2018
Accepted: 14 May 2018
Published: 14 August 2018
Julius Ross
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
United Kingdom
David Witt Nyström
Department of Mathematical Sciences
Chalmers University of Technology and the University of Gothenburg