TAILIEUCHUNG - On the solvability of the Riemann boundary value problem in Morrey-Hardy classes
This work considers the Riemann boundary value problem with the piecewise continuous coefficient in Morrey–Hardy classes. Under some conditions on the coefficient, the Fredholmness of this problem is studied and the general solution of homogeneous and nonhomogeneous problems in Morrey–Hardy classes is constructed. | Turk J Math (2016) 40: 1085 – 1101 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article On the solvability of the Riemann boundary value problem in Morrey–Hardy classes Bilal BILALOV∗, Telman GASYMOV, Aida GULIYEVA Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan Received: • Accepted/Published Online: • Final Version: Abstract: This work considers the Riemann boundary value problem with the piecewise continuous coefficient in Morrey– Hardy classes. Under some conditions on the coefficient, the Fredholmness of this problem is studied and the general solution of homogeneous and nonhomogeneous problems in Morrey–Hardy classes is constructed. Key words: Morrey–Hardy classes, Riemann problem 1. Introduction The concept of Morrey space was introduced by Morrey in 1938. Since then, various problems related to this space have been intensively studied. Playing an important role in the qualitative theory of elliptic differential equations (see, for example, [10, 13]), this space also provides a large class of examples of mild solutions to the Navier–Stokes system [9]. In the context of fluid dynamics, Morrey spaces have been used to model fluid flow when vorticity is a singular measure supported on certain sets in Rn [4]. There appeared lately a large number of research works that considered fundamental problems of the theory of differential equations, potential theory, maximal and singular operator theory, approximation theory, etc. in these spaces (see, for example, [3] and the references above). More details about Morrey spaces can be found in [11,14]. In view of the aforesaid, there has recently been a growing interest in the study of various problems in Morrey-type spaces. For example, some problems of harmonic analysis and approximation theory were considered in [1,5–8,12]. In this work, we consider the .
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