Abstract:
We consider boundary-value problems in the upper half-plane for second-order
elliptic systems with constant higher coefficients. Using the Bitsadze
transformation, we reduce these problems to equivalent problems for analytic
functions. This approach enables us to obtain explicit formulae for the
solutions of basic boundary-value problems and to study the Fredholm solubility
of these problems. (In particular, we obtain an analytic expression for the
index.) We work in weighted Hölder and Hardy spaces.
\Bibitem{Sol06}
\by A.~P.~Soldatov
\paper Second-order elliptic systems in the half-plane
\jour Izv. Math.
\yr 2006
\vol 70
\issue 6
\pages 1233--1264
\mathnet{http://mi.mathnet.ru/eng/im692}
\crossref{https://doi.org/10.1070/IM2006v070n06ABEH002345}
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Linking options:
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This publication is cited in the following 15 articles:
A. B Rasulov, “Influence of Nonisolated Singularities in a Lower-Order Coefficient of the Bitsadze Equation on the Statement of Boundary Value Problems”, Differentsialnye uravneniya, 59:10 (2023), 1385
A. B. Rasulov, “Influence of Nonisolated Singularities in a Lower-Order Coefficient of the Bitsadze Equation on the Statement of Boundary Value Problems”, Diff Equat, 59:10 (2023), 1384
Zhapsarbayeva L., Ospanov K., “Solvability of Nonlinear Problem For Some Second-Order Nonstrongly Elliptic System”, Complex Var. Elliptic Equ., 66:6-7 (2021), 1073–1083
A. P. Soldatov, Trends in Mathematics, Analysis as a Life, 2019, 279
Gryshchuk S.V., Plaksa S.A., “A Schwartz-Type Boundary Value Problem in a Biharmonic Plane”, Lobachevskii J. Math., 38:3, SI (2017), 435–442
A. P. Soldatov, “Mixed problem of plane orthotropic elasticity in a half-plane”, Diff Equat, 52:6 (2016), 798
A. P. Soldatov, “Generalized potentials of double layer in plane theory of elasticity”, Eurasian Math. J., 5:2 (2014), 78–125
Rajabov N.R., Rasulov A.B., “Linear Transmission Problem For a Bitsadze System With a Supersingular Circle”, Differ. Equ., 50:4 (2014), 526–532
A. Soldatov, “The Neumann problem for elliptic systems on a plane”, Journal of Mathematical Sciences, 202:6 (2014), 897–910
A. B. Rasulov, “Dirichlet and Hilbert problems for elliptic systems of second and third orders with a supersingular point”, Journal of Mathematical Sciences, 189:2 (2012), 257–273
Rasulov A.B., “Zadachi tipa Dirikhle dlya nekotorykh modelnykh uravnenii ellipticheskogo tipa so sverkhsingulyarnoi tochkoi”, Vestn. Mosk. energeticheskogo in-ta, 2010, no. 6, 47–53
A. P. Soldatov, “Hardy space of solutions of elliptic systems on the plane”, Journal of Mathematical Sciences, 160:1 (2009), 103–115
A. P. Soldatov, E. A. Abapolova, “Lamé system of elasticity theory in a plane orthotropic medium”, Journal of Mathematical Sciences, 157:3 (2009), 387–394
A. P. Soldatov, “The Hardy space of solutions to first-order elliptic systems”, Dokl. Math., 76:2 (2007), 660