Generalized integration over non-recifiable flat curves and boundary value problems

Abstract

The review discusses two closely related problems: the solution of the Riemann boundary value problem for analytic functions and some of their generalizations in areas of the complex plane with non-rectifiable boundaries, and the construction of a generalization of the curvilinear integral to non-rectifiable curves that preserves properties important for complex analysis. This work reflects the current state of the issue, and many of the results presented in it were obtained quite recently. At the end of the article, readers are offered a number of unsolved problems, each of which can serve as a starting point for scientific research.