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On a method of constructing the solutions of boundary-value problems of the theory of bendings of surfaces of positive curvature

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A new method is proposed for constructing the solutions of boundary-value problems of Riemann-Hilbert type for noncanonical linear and quasilinear first-order elliptic systems in a simply connected bounded region of the plane. For a linear boundary condition we obtain complete results; for a nonlinear boundary condition we study the solvability “in a neighborhood of zero.” Applications are given to the problem of isometric transformations of a surface diffeomorphic to the disk and having positive curvature all the way to the boundary under prescribed boundary conditions.

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Additional information

Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 56–82.

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Klimentov, S.B. On a method of constructing the solutions of boundary-value problems of the theory of bendings of surfaces of positive curvature. J Math Sci 51, 2230–2248 (1990).

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  • Boundary Condition
  • Elliptic System
  • Linear Boundary
  • Nonlinear Boundary
  • Complete Result