A Brief Approach to a Riemann-Hilbert Problem on Quasi-circles

Citation:

Tailiang LIU,Yuliang SHEN.A Brief Approach to a Riemann-Hilbert Problem on Quasi-circles[J].Chinese Annals of Mathematics B,2024,45(6):971~978
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Authors:

Tailiang LIU; Yuliang SHEN

Foundation:

the National Natural Science Foundation of China (No. 12171346).
Abstract: The authors introduce the Sobolev space H 1/2 (Γ) on a quasi-circle Γ and give a fast approach to the jump formula which gives a decomposition of an element in H 1/2 (Γ) as the boundary values of two Dirichlet functions in the complementary domains of Γ.

Keywords:

Sobolev space, Dirichlet space, Quasi-circle, Quasiconformal mapping

Classification:

30C62
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