Topological Methods in the Theory of Functions of a Complex Variable: II. Boundary Values and Integral Characteristics of Interior Transformations and Pseudo-Harmonic Functions

1945 ◽  
Vol 46 (4) ◽  
pp. 625 ◽  
Author(s):  
Marston Morse ◽  
Maurice Heins
Keyword(s):  
Complex Variable ◽  
Harmonic Functions ◽  
Boundary Values ◽  
Topological Methods ◽  
Integral Characteristics

scholarly journals On the boundary values of harmonic functions

1968 ◽  
Vol 132 (2) ◽  
pp. 307-307 ◽  
Author(s):  
Richard A. Hunt ◽  
Richard L. Wheeden
Keyword(s):  
Harmonic Functions ◽  
Boundary Values

scholarly journals P-harmonic dimensions on ends

1993 ◽  
Vol 132 ◽  
pp. 131-139
Author(s):  
Michihiko Kawamura ◽  
Shigeo Segawa
Keyword(s):  
Riemann Surface ◽  
Boundary Component ◽  
Harmonic Functions ◽  
Ideal Boundary ◽  
Boundary Values ◽  
Hölder Continuous ◽  
Closed Curves ◽  
Open Riemann Surface ◽  
Relative Boundary ◽  
Bounded Harmonic Functions

Consider an end Ω in the sense of Heins (cf. Heins [3]): Ω is a relatively non-compact subregion of an open Riemann surface such that the relative boundary ∂Ω consists of finitely many analytic Jordan closed curves, there exist no non-constant bounded harmonic functions with vanishing boundary values on ∂Ω and Ω has a single ideal boundary component. A density P = P(z)dxdy (z = x + iy) is a 2-form on Ω∩∂Ω with nonnegative locally Holder continuous coefficient P(z).

Sign in / Sign up

Export Citation Format

Share Document