We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is and the right hand side has a density in for some p > 1, and prove the Hölder continuity of the solution.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-2-1,
author = {Mohamad Charabati},
title = {H\"older regularity for solutions to complex Monge-Amp\`ere equations},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {109-127},
zbl = {1330.32012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-2-1}
}
Mohamad Charabati. Hölder regularity for solutions to complex Monge-Ampère equations. Annales Polonici Mathematici, Tome 113 (2015) pp. 109-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-2-1/