The Riemann – Hilbert boundary value problem for elliptic systems of the orthogonal type in R3
https://doi.org/10.29235/1561-2430-2020-56-1-7-16
Abstract
In this paper, a class of elliptic systems of four 1st order differential equations of the orthogonal type in R3 is considered. For such systems we study the issue of regularizability of the Riemann – Hilbert boundary value problem in an arbitrary limited simply-connected region with a smooth boundary in R3. Using the coefficients of the elliptic system and the matrix of the boundary operator, a special vector field is constructed, and its not entering the tangent plane in any point of the boundary provides the Lopatinski condition of the regularizability of the boundary value problem. The obtained condition permits to prove that the set of regularizable Riemann – Hilbert boundary value problems for the considered class of systems has two components of homotopic connectedness, and the index of an arbitrary regularizable problem equals to minus one.
About the Authors
A. I. Basik
Brest State A. S. Pushkin University
Belarus
Belarus
Aliaxandr I. Basik – Ph. D. (Physics and Mathematics)
21, Kosmonavtov Boulevard, 224016, BrestE. V. Hrytsuk
Brest State A. S. Pushkin University
Belarus
Belarus
Evgenij V. Hrytsuk – Ph. D. (Physics and Mathematics)
21, Kosmonavtov Boulevard, 224016, Brest
T. A. Hrytsuk
Brest State A. S. Pushkin University
Belarus
Belarus
Tatsiana A. Hrytsuk – Undergraduate Student
21, Kosmonavtov Boulevard, 224016, BrestReferences
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