Geodesic
Zigzag-like and spiral-like arcs in boundary-value problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 39-47

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It the paper is dealing with curvilinear integrals over non-smooth paths with application in boundary-value problems. We show that geometry of end-points of the path is of importance for solvability of homogeneous Riemann boundary-value problem on this arc. On a zigzag-like path the numbers of solutions and conditions of solvability are the same as for smooth arcs, but for spiral-like paths these numbers can vary.
Keywords: non-smooth path, curvilinear integral, Cauchy type integral, Riemann boundary-value problem. 
@article{IVM_2019_7_a3,
     author = {B. A. Kats},
     title = {Zigzag-like and spiral-like arcs in boundary-value problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {39--47},
     publisher = {mathdoc},
     number = {7},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_7_a3/}
}
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B. A. Kats. Zigzag-like and spiral-like arcs in boundary-value problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 39-47. http://geodesic.mathdoc.fr/item/IVM_2019_7_a3/