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- W36735809 abstract "In Section 1, we present a solution of the following boundary value problem: find an analytic function Φon the plane cut along a closed piecewisesmooth curve Γ which is represented by a Cauchy type integral with a density from the Grand Lebesgue Space $$ L^{p)},theta(Gamma)(1 < p < infty, 0 < theta < infty) $$ and whose boundary values satisfy the conjugacy condition $$ Phi^{+}(t)=G(t)Phi^{-}(t)+g(t),quad t in Gamma $$ Here G and g are functions defined on Γ such that G is a piecewise continuous function, $$ G(t)neq 0 $$ and $$ g in L^{{p}),theta}(Gamma) $$ The conditions for the problem to be solvable are established and the solutions are constructed in explicit form. In Section 2, the Dirichlet problem for harmonic functions, real parts of Cauchy type integrals with densities from weighted generalized Grand Lebesgue Spaces is studied when boundary data belong to the same space." @default.
- W36735809 created "2016-06-24" @default.
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- W36735809 date "2013-01-01" @default.
- W36735809 modified "2023-09-26" @default.
- W36735809 title "The Riemann and Dirichlet Problems with Data from the Grand Lebesgue Spaces" @default.
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- W36735809 doi "https://doi.org/10.1007/978-3-0348-0516-2_13" @default.
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