#### 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 ${L}^{p}$ 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