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arXiv · 2604.06437

Rarity of $\boldsymbol{\mathcal{C}^{1,1}}$ solutions to the complex Monge--Amp\`ere equation on weakly pseudoconvex domains

Gautam Bharali·Rumpa Masanta
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Abstract

We show that on any weakly pseudoconvex $B$-regular domain, the classical Dirichlet problem for the complex Monge--Amp\`ere equation with $\mathcal{C}^\infty$-smooth data does not in general admit $\mathcal{C}^{1,1}$-smooth solutions. This working draft is a prelude to potential-theoretic solutions to some extension problems for mappings that were thought to rely on such $\mathcal{C}^{1,1}$-smooth solutions.

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Gautam Bharali, Rumpa Masanta. 2026-04-07. Rarity of $\boldsymbol{\mathcal{C}^{1,1}}$ solutions to the complex Monge--Amp\`ere equation on weakly pseudoconvex domains. https://arxiv.org/abs/2604.06437

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