On the definition of the Monge-Ampère operator in ℂ2

By Zbigniew Blocki. 2004

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We show that if u is a plurisubharmonic function defined on an open subset Ω of ℂ2 then the Monge-Ampère measure (ddcu)2 can be well defined if and only if u belongs to the Sobolev space W1,2loc(Ω).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/626f08aaab0dbf31aa64baf85a0412b156ed0bf3