Dirichlet problem for plurisubharmonic functions on bounded quasi B-regular domains in ℂⁿ

2025/09/15 by Dieu, N. Q., Tang Van Long, Long, T. V. +2
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2509.12063

openalex publication_date 2025/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate existence and uniqueness of maximal plurisubharmonic functions on bounded domains with boundary data that are not assumed to be continuous or bounded. The result is applied to approximate (possibly unbounded from above) plurisubharmonic functions by continuous quasi upper bounded ones. A key step in our approach is to explore continuity of the Perron-Bremermann envelope of plurisubharmonic functions that are dominated by a given function ϕ defined on the closure of the domain.

Citations

• Plurisubharmonic functions with discontinuous boundary behavior
• Continuity of envelopes of unbounded plurisubharmonic functions
• Approximation of plurisubharmonic functions on complex varieties
• Characterizations of boundary pluripolar Hulls
• Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves

Related

• Continuity of envelopes of unbounded plurisubharmonic functions
• The Bremermann-Dirichlet problem for unbounded domains of Cⁿ
• Plurisubharmonic Approximation and Boundary Values of Plurisubharmonic Functions
• Some properties of maximal plurisubharmonic function
• On the conditional plurisubharmonic envelopes of bounded functions