Boundary value problems in Hardy weighted spaces.

      Аннотация: In this book there are investigated boundary value problems for elliptic equations in the unit circle. Riemann, Riemann-Hilbert and Dirichlet problems are solved in the Lebesgue weighted spaces. This kind of problems arose during the investigation of boundary value problems of partial differential elliptic equations which have applications in a lot of disciplines of theoretical physics, such as aerodynamics, hydrodynamics, electrodynamics, elasticity theory, etc. Famous mathematicians M. Krein, N. Muskhelishvili, F. Gakhov, H. Hayrapetyan, N. Tovmasyan and others investigated this kind of problems with boundary conditions in Holder classes and some specific Lebesgue spaces. This book is a generalisation of the classical results, the problems are solved for both continuous and discontinuous in the sense of Holder coefficients and the solutions are written in explicit form.

Ключевые слова: Boundary value problems, factorization, weighted spaces, Cauch type integral, biharmonic functions, Holder class of functions