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arXiv · 2604.27469

Estimates of the modulus of continuity of the logarithmic double layer potential in the closure of domain

Sergiy Plaksa·Alexander Sarana
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Abstract

We obtain estimates of the modulus of continuity for the real part of the Cauchy-type integral in the closure of domain bounded by an Ahlfors-regular integration curve. These estimates are more exact than the well-known Zygmund estimate for the modulus of continuity of the Cauchy-type integral. The accuracy of estimates is proved by constructing an example of a curve and an integral density for which the specified estimates are exact with respect to the order of smallness.

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Sergiy Plaksa, Alexander Sarana. 2026-04-30. Estimates of the modulus of continuity of the logarithmic double layer potential in the closure of domain. https://arxiv.org/abs/2604.27469

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