The complex Monge-Amp\'ere equation on the complement of a divisor
Abstract
We consider the complex Monge-Amp\'ere equation on complete K\"ahler manifolds with cusp singularity along a divisor when the right hand side F has rather weak regularity. We proved that when the right hand side F is in some weighted W1,p0 space for p0 > 2n, the Monge-Amp\'ere equation has a classical W3,p0 solution.
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