scholarly journals Boundary Integral Formula for Harmonic Functions on Riemann Surfaces

2020 ◽  
Vol 20 (2) ◽  
pp. 235-253
Author(s):  
Peter L. Polyakov
Keyword(s):  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Integral Formula ◽  
Boundary Integral ◽  
Boundary Integral Formula

Boundary integral formula of elastic problems in circle plane

2005 ◽  
Vol 26 (5) ◽  
pp. 604-608 ◽  
Author(s):  
Dong Zheng-zhu ◽  
Li Shun-cai ◽  
Yu De-hao
Keyword(s):  
Integral Formula ◽  
Boundary Integral ◽  
Circle Plane ◽  
Boundary Integral Formula

scholarly journals RETRACTED ARTICLE: An augmented Riesz decomposition method for sharp estimates of certain boundary value problem

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Jiaofeng Wang ◽  
Bin Huang ◽  
Nanjundan Yamini
Keyword(s):  
Boundary Value Problem ◽  
Lower Bounds ◽  
Harmonic Functions ◽  
Decomposition Method ◽  
Integral Condition ◽  
Boundary Integral ◽  
Sharp Estimates ◽  
Riesz Decomposition ◽  
Retracted Article ◽  
Riesz Decomposition Method

AbstractIn this paper, by using an augmented Riesz decomposition method, we obtain sharp estimates of harmonic functions with certain boundary integral condition, which provide explicit lower bounds of functions harmonic in a cone. The results given here can be used as tools in the study of integral equations.

A Maximum Principle for Dirichlet-Finite Harmonic Functions on Riemannian Spaces

1970 ◽  
Vol 22 (4) ◽  
pp. 855-862
Author(s):  
Y. K. Kwon ◽  
L. Sario
Keyword(s):  
Maximum Principle ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Decomposition Theorem ◽  
Higher Dimensions ◽  
Integral Representations ◽  
Classification Theory ◽  
Topological Properties ◽  
Harmonic Decomposition ◽  
Bounded Harmonic Functions

Representations of harmonic functions by means of integrals taken over the harmonic boundary ΔR of a Riemann surface R enable one to study the classification theory of Riemann surfaces in terms of topological properties of ΔR (cf. [6; 4; 1; 7]). In deducing such integral representations, essential use is made of the fact that the functions in question attain their maxima and minima on ΔR.The corresponding maximum principle in higher dimensions was discussed for bounded harmonic functions in [3]. In the present paper we consider Dirichlet-finite harmonic functions. We shall show that every such function on a subregion G of a Riemannian N-space R attains its maximum and minimum on the set , where ∂G is the relative boundary of G in R and the closures are taken in Royden's compactification R*. As an application we obtain the harmonic decomposition theorem relative to a compact subset K of R* with a smooth ∂(K ∩ R).

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