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1992 | 27 | 1 | 45-63
Tytuł artykułu

Estimates of solutions to linear elliptic systems and equations

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Whenever nonlinear problems have to be solved through approximation methods by solving related linear problems a priori estimates are very useful. In the following this kind of estimates are presented for a variety of equations related to generalized first order Beltrami systems in the plane and for second order elliptic equations in $ℝ^m$. Different types of boundary value problems are considered. For Beltrami systems these are the Riemann-Hilbert, the Riemann and the Poincaré problem, while for elliptic equations the Dirichlet problem as well as entire solutions are involved.
Słowa kluczowe
Rocznik
Tom
27
Numer
1
Strony
45-63
Opis fizyczny
Daty
wydano
1992
Twórcy
  • I. Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, D-1000 Berlin 33, Germany
Bibliografia
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  • [7] H. Begehr and R. P. Gilbert, On Riemann boundary value problems for certain linear elliptic systems in the plane, J. Differential Equations 32 (1979), 1-14.
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  • [12] H. Begehr and G. N. Hile, Schauder estimates and existence theory for entire solutions of linear elliptic equations, Proc. Roy. Soc. Edinburgh 110A (1988), 101-123.
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  • [16] H. Begehr and G. C. Hsiao, The Hilbert boundary value problem for nonlinear elliptic systems, Proc. Roy. Soc. Edinburgh 94A (1983), 97-112.
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  • [21] H. Begehr and Z. Y. Xu, Nonlinear half-Dirichlet problems for first order elliptic equations in the unit ball of $ℝ^m$ (m ≥ 3), Appl. Anal., to appear.
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  • [32] B. Bojarski, Quasiconformal mappings and general structural properties of systems of non-linear equations elliptic in the sense of Lavrentiev, Symposia Math. 18 (1976), 485-499.
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  • [34] F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Pitman, London 1982.
  • [35] D. Q. Dai, On an initial boundary value problem for nonlinear pseudoparabolic equations with two space variables, Complex Variables Theory Appl., to appear.
  • [36] R. Delanghe, F. Sommen and Z. Y. Xu, Half-Dirichlet problems for powers of the Dirac operator in the unit ball of $ℝ^m$ (m ≥ 3), Bull. Soc. Math. Belg. Sér. B 42 (1990), 409-429.
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  • [42] R. P. Gilbert and G. N. Hile, Generalized hypercomplex function theory, Trans. Amer. Math. Soc. 195 (1974), 1-29.
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  • [49] W. Tutschke, Reduction of the problem of linear conjugation for first order nonlinear elliptic systems in the plane to an analogous problem for holomorphic functions, in: Lecture Notes in Math. 798, Springer, Berlin 1980, 446-455.
  • [50] W. Tutschke, Partielle Differentialgleichungen, Teubner, Leipzig 1983.
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  • [52] V. S. Vinogradov, On a boundary value problem for linear elliptic systems of first order in the plane, Dokl. Akad. Nauk SSSR 118 (1958), 1059-1062 (in Russian).
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  • [56] G.-C. Wen and H. Begehr, Boundary Value Problems for Elliptic Equations and Systems, Longman, Essex 1990.
  • [57] W. Wendland, An integral equation method for generalized analytic functions, in: Constructive and Computational Methods for Differential and Integral Equations, Lecture Notes in Math. 430, Springer, Berlin 1974, 414-452.
  • [58] W. Wendland, On the imbedding method for semilinear first order elliptic systems and related finite element methods, in: Continuation Methods, Acad. Press, New York 1978, 277-336.
  • [59] W. Wendland, Elliptic Systems in the Plane, Pitman, London 1979.
  • [60] J. Wloka, Funktionenanalysis und Anwendungen, de Gruyter, Berlin 1971.
  • [61] Z. Xu, Boundary value problems and function theory for spin-invariant differential operators, thesis, State University of Ghent, Gent 1989.
Typ dokumentu
Bibliografia
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