Estimates of the modulus of continuity of the logarithmic double layer potential
Abstract
For the real part of the Cauchy-type integral, which is known to be the logarithmic double layer potential,
we obtain estimates of the modulus of continuity 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 for the logarithmic double layer potential 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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S. Plaksa, A. Sarana, Estimates of the Modulus of Continuity of the Logarithmic Double Layer Potential in the Closure of Domain, arXiv:2604.27469 [math.CV] (2026). https://doi.org/10.48550/arXiv.2604.27469
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