Abstract:
A general boundary value problem, encompassing from a unified viewpoint a broad circle of local and nonlocal boundary value problems, is studied for elliptic systems with real, constant (and only leading) matrix coefficients. A method is given for the equivalent reduction of this problem to a system of boundary equations. The considerations are carried out in domains with piecewise smooth boundaries and in weighted spaces. A Noetherian criterion and an index formula for this problem are established, and the asymptotics of its solution in a neighborhood of corner points is described.
Citation:
A. P. Soldatov, “A function theorety method in elliptic problems in the plane. II. The piecewise smooth case”, Russian Acad. Sci. Izv. Math., 40:3 (1993), 529–563
This publication is cited in the following 16 articles:
Mitin S.P. Soldatov A.P., “Bitsadze-Samarski Problem For Elliptic Systems of Second Order”, Azerbaijan J. Math., 11:1 (2021), 154–168
A. H. Babayan, “On a Dirichlet problem for one improperly elliptic equation”, Complex Variables and Elliptic Equations, 64:5 (2019), 825
Armenak H. Babayan, Seyran H. Abelyan, Springer Proceedings in Mathematics & Statistics, 291, Modern Methods in Operator Theory and Harmonic Analysis, 2019, 317
Yu. A. Bogan, “The Dirichlet Problem for an Elliptic System of Second-Order Equations with Constant Real Coefficients in the Plane”, Math. Notes, 104:5 (2018), 636–641
S. I. Bezrodnykh, V. I. Vlasov, “Singular Riemann–Hilbert problem in complex-shaped domains”, Comput. Math. Math. Phys., 54:12 (2014), 1826–1875
H.M. Hayrapetyan, P.E. Meliksetyan, “On normal solvability of a Dirichlet-type problem for a third-order improperly elliptic equation”, Complex Variables and Elliptic Equations, 2011, 1
Kovaleva L.A., Soldatov A.P., “On a Nonlocal Problem in Function Theory”, Differ. Equ., 46:3 (2010), 400–414
Vashchenko O.V., Soldatov A.P., “The Hardy Space of Solutions of the Generalized Beltrami System”, Differ. Equ., 43:4 (2007), 503–506
Soldatov A.P., “On the Index of the Dirichlet Problem for Elliptic Systems on the Plane”, Differ. Equ., 42:8 (2006), 1156–1169
Soldatov A.P., “The Bitsadze-Samarskii problem for Douglis analytic functions”, Differential Equations, 41:3 (2005), 416–428
Soldatov A., “Weighted Hardy Classes of Analytic Functions”, Differ. Equ., 38:6 (2002), 855–864
M. M. Sirazhudinov, A. G. Magomedov, V. G. Magomedova, “Boundary-value problems for general elliptic systems in the plane. II”, Izv. Math., 64:3 (2000), 601–651
Soldatov A., “Riemann–Hilbert Problem for the Lavrent'Ev-Bitsadze System”, Differ. Equ., 34:12 (1998), 1656–1666
Mitin S., “Representation of Solutions of Anisotropic Elasticity”, Differ. Equ., 34:1 (1998), 95–102
Mitin S., Soldatov A., “Solvability of the Generalized Mixed Problem”, Differ. Equ., 32:3 (1996), 388–392
Soldatov A., “The Problems of Dirichlet Type for Lavrentev-Bitsadze Equation .2. Existence Theorems”, Dokl. Akad. Nauk, 333:1 (1993), 16–18