In this paper we are interested in studying the Perron–Bremermann envelope of plurisubharmonic functions. We give a sufficient condition for the envelope to be Hölder continuous.
Bedford, E., Taylor, B.A.: The Dirichlet problem for a complex Monge–Ampère equation. Invent. Math. 37(1), 1–44 (1976)
Bedford, E., Taylor, B.A.: A new capacity for plurisubharmonic functions. Acta Math. 149, 1–40 (1982)
Bremermann, H.J.: On a generalized Dirichlet problem for plurisubharmonic functions and pseudo-convex domains. Characterization of Šilov boundaries....
Cegrell, U.: The general definition of the complex Monge–Ampère operator. Ann. Inst. Fourier (Grenoble) 54(1), 159–179 (2004)
Cegrell, U.: A general Dirichlet problem for the complex Monge–Ampère operator. Ann. Pol. Math. 94(2), 131–147 (2008)