Direct and Inverse Problems for the Simple Layer Logarithmic Potential

Abstract

© 2020, Allerton Press, Inc. With the help of Cauchy-type integrals, a newderivation of integral equations for solving logarithmic potentialproblems is given. A variant of the inverse logarithmic potentialproblem with two starlike solutions is analyzed; it contains fewerparameters than those considered by I.M. Rapoport. A criterion forthe interior simple layer potential to be identically constant isobtained.