Weak solutions to the quaternionic Monge-Ampère equation

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 two which turns out to be less than an integrability exponent of the fundamental solution.

arXiv commentminor corrections, final version, to appear in Analysis & PDE

References in corpus (6)

• Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables
• A priori estimates for the complex Hessian equations
• Quaternionic Monge-Ampere equations
• On quaternionic Monge-Ampere operator, closed positive currents and Lelong-Jensen type formula on quaternionic space
• Potential theory in several quaternionic variables
• Dirichlet Problem of Quaternionic Monge-Ampère Equations

Cited by in corpus (2)

• On the Alesker-Verbitsky conjecture on hyperKähler manifolds
• Sharp uniform bound for the quaternionic Monge-Ampere equation on hyperhermitian manifolds