Well-Posedness of Jump Problem on Non-rectifiable Curves

Abstract

© 2018, Springer Nature Switzerland AG. We investigate the well-posedness of a jump problem on non-rectifiable curves with Hölder boundary data. The jump problem is a special case of Riemann boundary value problem. However, the classic results are obtained in the case of piecewise smooth boundary. There are some results for non-rectifiable boundary (see our previous papers in bibliography), but still there is a large field of questions waiting for answers.