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This article is available for purchase or by subscription. See below.
Abstract
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We solve the Dirichlet problem for the quaternionic Monge–Ampère
equation with a continuous boundary data and the right-hand side in
for
. This is the
optimal bound on
.
We prove also that the local integrability exponent of quaternionic plurisubharmonic
functions is 2, which turns out to be less than an integrability exponent of the
fundamental solution.
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Keywords
Monge–Ampère equation, pluripotential theory, quaternionic
plurisubharmonic functions
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Mathematical Subject Classification 2010
Primary: 32U05, 32U15, 35D30, 35J60
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Milestones
Received: 19 July 2018
Revised: 9 May 2019
Accepted: 11 July 2019
Published: 12 September 2020
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