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arXiv · 1704.04350

The complex Monge-Amp\`ere equation on weakly pseudoconvex domains

Luca Baracco·Tran Vu Khanh·Stefano Pinton
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Abstract

We show here a "weak" H\"older-regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Amp\`{e}re equation with data in the $L^p$ space and the boundary of the domain satisfying an $f$-property. The $f$-property is a potential-theoretical condition which holds for all pseudoconvex domains of finite type and many examples of infinite type.

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Luca Baracco, Tran Vu Khanh, Stefano Pinton. 2017-04-14. The complex Monge-Amp\`ere equation on weakly pseudoconvex domains. https://arxiv.org/abs/1704.04350

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