Curvilinear integrals of discontinuous functions over nonrectifiable paths and Riemann boundary-value problem

Abstract

© 2019 John Wiley & Sons, Ltd. We study a generalization of the concept of curvilinear integral for the case where path of integration is nonrectifiable, and integrand has discontinuities. Then we apply that integrals for solving of the Riemann boundary-value problem for domains with nonrectifiable boundaries and discontinuous boundary data. The research is supported by RFBR (grant 18-31-00060) and is performed according to a special programme of the Russian government supporting research at Kazan Federal University. Mathematical Methods in the Applied Sciences journal encourages authors to share the data and other artifacts supporting the results in the paper by archiving it in an appropriate public repository. Authors may provide a data availability statement, including a link to the repository they have used, in order that this statement can be published in their paper. Shared data should be cited.