A boundary integral method for the Riemann–Hilbert problem on multiply connected domains

Abstract: Let $G$ be a multiply connected domain in the extended complex plane and let $A$ be a complex function on the boundary $\partial G$ with $A\ne0$. For a given real function $\gamma$ on $\partial G$, the Riemann--Hilbert (RH) boundary value problem requires determining a function $f$ analytic in $G$ (vanishing at infinity for unbounded $G$), continuous in the closure $\overline{G}$, and satisfying the boundary condition Re$[Af]=\gamma$ on $\partial G.$

A boundary integral method for solving the above RH problem will be presented in this talk. The method is based on an integral equation known as {the boundary integral equation with the generalized Neumann kernel}. Applications of the method will be also presented.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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