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Weakly Solutions to the Complex Monge–Ampère Equation on Bounded Plurifinely Hyperconvex Domains

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Let $$\mu $$μ be a non-negative measure defined on bounded $${\mathcal {F}}$$F-hyperconvex domain $$\Omega $$Ω. We are interested in giving sufficient conditions on $$\mu $$μ such that we can find… Click to show full abstract

Let $$\mu $$μ be a non-negative measure defined on bounded $${\mathcal {F}}$$F-hyperconvex domain $$\Omega $$Ω. We are interested in giving sufficient conditions on $$\mu $$μ such that we can find a plurifinely plurisubharmonic function satisfying NP$$(dd^c u)^n =\mu $$(ddcu)n=μ in QB$$(\Omega )$$(Ω).

Keywords: solutions complex; amp equation; complex monge; weakly solutions; monge amp; equation bounded

Journal Title: Complex Analysis and Operator Theory
Year Published: 2018

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