Geodesic
Smooth regularization of plurisubharmonic functions
Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 312-320 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of approximating a given plurisubharmonic function by smooth plurisubharmonic functions. We propose a new constructive approximation method that permits one to obtain more detailed information about the approximating functions. Thus a function $u\in\operatorname{PSH}(\mathbb C^n)$ having finite growth order can be approximated by smooth functions $v\in\operatorname{PSH}(\mathbb C^n)$ so that the difference $|v-u|$ has almost logarithmic growth (Theorem 2). It can also be approximated so that the difference $|v-u|$ has a power-law growth; in this case, however, power-law estimates on $|\operatorname{grad}v|$ appear (Theorem 3). 
@article{MZM_1997_62_2_a12,
     author = {R. S. Yulmukhametov},
     title = {Smooth regularization of plurisubharmonic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {312--320},
     year = {1997},
     volume = {62},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a12/}
}
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R. S. Yulmukhametov. Smooth regularization of plurisubharmonic functions. Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 312-320. http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a12/

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