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The paper considers a Dirichlet-type boundary value problem for the elliptic equation ∂ m+n u ∂z ¯ m ∂z n =0,∂u ∂z ¯≡1 2∂u ∂x+i∂u ∂y,∂u ∂z≡1 2∂u ∂x-i∂u ∂y in a multiply connected domain. The problem is reduced to a Dirichlet problem for the n-harmonic equation. An existence theorem is proved.

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The paper investigates a Riemann-Hilbert type problem for second order nonregular elliptic equation in weighted spaces. It
is established that the number of linearly independent solutions of the homogeneous problem and the number of conditions on
the boundary functions depend not only on the order of singularity of the weight function and coefficient indices of the considered
problem, but also on the behavior of these functions at singular points.

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