Vol. 13, No. 6, 2020

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Weak solutions to the quaternionic Monge–Ampère equation

Marcin Sroka

Vol. 13 (2020), No. 6, 1755–1776
Abstract

We solve the Dirichlet problem for the quaternionic Monge–Ampère equation with a continuous boundary data and the right-hand side in Lp for p > 2. This is the optimal bound on p. 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.

Keywords
Monge–Ampère equation, pluripotential theory, quaternionic plurisubharmonic functions
Mathematical Subject Classification 2010
Primary: 32U05, 32U15, 35D30, 35J60
Milestones
Received: 19 July 2018
Revised: 9 May 2019
Accepted: 11 July 2019
Published: 12 September 2020
Authors
Marcin Sroka
Faculty of Mathematics and Computer Science
Jagiellonian University
Kraków
Poland