A mixed boundary problem of magnetized semiconductor physics in interior of domain

A mixed boundary problem has been considered for harmonic functions in a multiply connected interior of domain. Some boundary curves obey the Dirichlet condition, the rest of the boundary curves satisfying a condition with an oblique derivative. To find the solution, a uniquely solvable Fredholm integral equation of second kind has been obtained. As a result, the existence of the unique solution of the problem in the domain of continuous functions has been proved.