Abstract
Let Ω be an m-hyperconvex domain of Cn and β be the standard Kähler form in Cn. We introduce finite energy classes of m-subharmonic functions of Cegrell type, Emp(Ω), p>0 and Fm(Ω). Using a variational method we show that the degenerate complex Hessian equation (ddcφ)m∧βn−m=μ has a unique solution in Em1(Ω) if and only if every function in Em1(Ω) is integrable with respect to μ. If μ has finite total mass and does not charge m-polar sets, then the equation has a unique solution in Fm(Ω).
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