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Riemann boundary value problem on nonrectifiable curves for certain Beltrami equations
Author(s) -
Katz D. B.,
Kats B. A.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4755
Subject(s) - mathematics , mathematical analysis , cauchy–riemann equations , type (biology) , simple (philosophy) , piecewise , boundary value problem , representation (politics) , riemann hypothesis , cauchy distribution , riemann problem , initial value problem , ecology , philosophy , epistemology , politics , political science , law , biology
In this paper, we obtain a Cauchy‐type integral representation to solve certain Beltrami equations and apply it for research of the Riemann boundary value problem for that equations on nonrectifiable contours. While more or less studied for piecewise smooth contours, for the case of nonrectifiable curve, this is a pioneer result. There is only one relatively simple type of Beltrami equation that is solved under such condition (see below). Our next goal is to achieve solutions for more types of the Beltrami equations on nonrectifiable curves.