Regularity of solutions to the quaternionic Monge-Ampère equation

Bibliographic description

punktacja MEiN [2020]: 100

title:	Regularity of solutions to the quaternionic Monge-Ampère equation
author:	Kołodziej Sławomir , Sroka Marcin
journal title:	Journal of Geometric Analysis
volume:	30
date of publication :	2020
pages:	2852-2864
ISSN:	1050-6926
eISSN:	1559-002X
DOI:	10.1007/s12220-020-00394-2
language:	English
journal language:	English
abstract in English:	The regularity of solutions to the Dirichlet problem for the quaternionic Monge-Ampère equation is discussed. We prove that the solution to the Dirichlet problem is Hölder continuous under some conditions on the boundary values and the quaternionic Monge-Ampère density from Lp(Ω) for p>2. As a step towards the proof, we provide a refined version of stability for the weak solutions to this equation.
keywords in English:	Monge-Ampere equation, pluripotential theory, subharmonic functions
affiliation:	Wydział Matematyki i Informatyki : Instytut Matematyki
type:	journal article
subtype:	academic paper