Abstract
The first, second and mixed fundamental boundary-value problems of elasticity theory are considered on an n-sheet Riemann surface with straight-line cuts joining the branch points. The cuts are such that their edges are situated in different planes. Complex potentials are constructed, asymptotic representations of the stresses and derivatives of the displacement components are obtained near the vertices of the cuts and invariant Γ- integrals /1/ are obtained, by the method of reduction to a matrix Riemann boundary-value problem. The first and second fundamental problems for an n= 2 Riemann surface were solved /2/ by the Riemann boundary-value problem method for a Riemann surface. For n=1 the results are identical with previously known results for a plane /3/.
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