On the Continuous Extension of the Logarithmic Double Layer Potential to Boundary of Domain

Explore the continuous extension of the logarithmic double layer potential to domain boundaries in this 47-minute HyperComplex Seminar talk. Delve into Prof. Sergiy Plaksa's analysis of closed rectifiable Jordan curves in the complex plane, focusing on interior and exterior domains. Examine the classical theory of logarithmic double layer potential for Lyapunov and Radon curves, and discover the necessary and sufficient conditions for continuous extension to Ahlfors-regular boundaries. Learn about the broader class of curves beyond Král's result and gain insights through illustrative examples. Enhance your understanding of key concepts including Cauchy-type integrals, Ahlfors-regular curves, Král curves, Radon curves, and Lyapunov curves.