Let Ω be a smoothly bounded domain in ℂ™ such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω at 0 in terms of the Hölder exponent of its Perron-Bremermann function with simple boundary data. We then use this to show that a smoothly bounded domain in ℂ2 is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Holder continuous boundary data is Hölder continuous.
ASJC Scopus subject areas
- Applied Mathematics