Bài toán Dirichlet cho các hàm hài hòa từ các lớp Smirnov có chỉ số biến trong các miền có biên mịn từng đoạn

C. Miranda, Partial Differential Equations of Elliptic Type, Springer, New York etc. (1970). N. Muskhelishvili, Singular Integral Equations. Boundary Value Problems in the Theory of Function and Some Applications of Them to Mathematical Physics [in Russian], Nauka, Moscow (1968). M. Dauge, Elliptic Boundary Value Problems on Corner Domains. Smoothness and Asymptotics of Solutions, Springer, Berlin (1988). V. Maz’ya and A. Soloviev, “L p -theory of boundary integral equations on a contour with outward peak,” Integral Equ. Operator Theory 32, No. 1, 75–100 (1998). V. Maz’ya and A. Soloviev, “A direct method for boundary integral equations on a contour with a peak,” Georgian Math. J. 10, No. 3, 573–593 (2003). L. Diening and M. Růzicka, “Calderón–Zygmund operators on generalized Lebesgue spaces L p(·) and problems related to fluid dynamics,” J. Reine Angew. Math. 563, 197–220 (2003). M. Růzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Springer, Berlin (2000). A. Yu. Karlovich, “Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces,” J. Integral Equ. Appl. 15, No. 3, 263–320 (2003). V. Kokilashvili, V. Paatashvili, and S. Samko, “Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in L p(·)(Γ),” Bound. Value Probl. No. 1, 43–71 (2005). V. Kokilashvili and V. Paatashvili, “The Dirichlet problem for harmonic functions in the Smirnov class with variable exponent,” Georgian Math. J. 14, No. 2, 289–299 (2007). V. Kokilashvili and V. Paatashvili, “The Riemann–Hilbert problem in weighted classes of Cauchy type integrals with density from L p(·)(Γ),” Complex Anal. Oper. Theory 2, No. 4, 569–591 (2008). V. Kokilashvili and V. Paatashvili, “The Riemann-Hilbert problem in a domain with piecewise smooth boundaries in weight classes of Cauchy type integrals with a density from variable exponent Lebesgue spaces,” Georgian Math. J. 16, No. 4, 737–755 (2009). G. Khuskivadze, V. Kokilashvili, and V. Paatashvili, “Boundary value problems for analytic and harmonic functions in domains with nonsmooth boundaries. Applications to conformal mappings,” Mem. Differ. Equ. Math. Phys. 14, 1–195 (1998). V. Kokilashvili and V. Paatashvili, “On Hardy classes of analytic functions with a variable exponent,” Proc. A. Razmadze Math. Inst. 142, 134–137 (2006). V. Kokilashvili and V. Paatashvili, “On variable Hardy and Smirnov classes of analytic functions,” Georgian Internat. J. Sci. 1, No. 2, 67–81 (2008). V. Kokilashvili and V. Paatashvili, “Weighted Hardy and Smirnov classes and the Dirichlet problem for a ring within the framework of variable exponent analysis,” Complex Variables and Elliptic Equations [Submitted] P. L. Duren, Theory of Hp Spaces, Academic Press, New York etc. (1970). V. Kokilashvili, V. Paatashvili, and S. Samko, “Boundedness in Lebesgue spaces with variable exponent of the Cauchy singular operator on Carleson curves,” In: Modern Operator Theory Applications, pp. 167–186, Birkhäuser, Basel (2007). S. Warschawski, “Über das Randverhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung,” Math. Z. 35, No. 1, 321–456 (1932).