TITLE:
Riemann Boundary Value Problems on the Curve of Parabola
AUTHORS:
Yanyan Lei, Hua Liu
KEYWORDS:
Riemann-Hilbert Problem, Plemelj Formula, The Cauchy-Type Integral
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.5,
May
29,
2023
ABSTRACT: In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type integral and Cauchy principal value integral on the Curve of Parabola at infinity. At the end, we discuss the Riemann boundary value problems for sectionally holomorphic functions with the Curve of Parabola as their jump curve and obtain the explicit form.