A Brief Approach to a Riemann-Hilbert Problem on Quasi-circles
Tailiang Liu , Yuliang Shen
Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (6) : 971 -978.
A Brief Approach to a Riemann-Hilbert Problem on Quasi-circles
The authors introduce the Sobolev space $H^{{1\over 2}}(\Gamma)$ on a quasi-circle Γ and give a fast approach to the jump formula which gives a decomposition of an element in $H^{{1\over 2}}(\Gamma)$ as the boundary values of two Dirichlet functions in the complementary domains of Γ.
Sobolev space / Dirichlet space / Quasi-circle / Quasiconformal mapping
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