Continuous extension to the boundary of a domain of the logarithmic double layer potential

S. A. Plaksa

Department of Complex Analysis and Potential Theory, Institute of Mathematics of the National Academy of Sciences of Ukraine, 3 Tereschenkivska St, 01024 Kyiv, Ukraine

Abstract: For the real part of the Cauchy-type integral that is known to be the logarithmic potential of the double layer, a necessary and sufficient condition for the continuous extension to the Ahlfors-regular boundary is established. Sufficient conditions involving subclasses of Ahlfors-regular curves are also considered. Illustrative examples are presented.

Keywords and phrases: logarithmic double layer potential, Cauchy-type integral, Ahlfors-regular curve, Král curve, Radon curve, Lyapunov curve.

MSC: 30E20, 31A10

Received: 12.09.2024

Language: English

DOI: 10.32523/2077-9879-2025-16-4-54-75