On the Noether property and index of certain two-dimensional singular integral equations with discontinuous coefficients (Q1333630)

We establish an effective Noether criterion for certain two-dimensional singular integral equations in a bounded simply connected domain in weighted Lebesgue space \(L^ p\) and find the formulas for evaluation of the index. The coefficient of the singular integral in the equation under consideration has a discontinuity of the form \((z/ | z |)^ n\) at the point \(z = 0\), where \(n\) is an integer number. The discontinuity essentially influences both the Noether properties and the index of the equation.