July 31, 2024Open Access

Singular Solutions to the Complex Monge-Amp\`ere Equation

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Abstract

We present an explicit pluripotential and viscosity solution to the complex Monge-Amp\`ere equation with constant right-hand side on D C^n-1\, (n 2), which lies merely in W^1, 2₋₎₂ W^2, 1₋₎₂ and is not even Dini continuous. Additionally, we exhibit two families of explicit entire toric solutions on Cⁿ with continuous H\"older exponent (0, 1) and W^2, p₋₎₂ exponent p (1, 2).

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Wang et al. (Wed,) studied this question.

synapsesocial.com/papers/68e5e6e9b6db64358757b47f https://doi.org/https://doi.org/10.48550/arxiv.2407.21667

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