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THE MIXED PROBLEM FOR HARMONIC FUNCTIONS OUTSIDE A CUT OF AN ARBITRARY SHAPE

    https://doi.org/10.1142/9789812794253_0133Cited by:0 (Source: Crossref)
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    Abstract:

    The problem for harmonic functions outside a cut of an arbitrary shape in a plane is studied. The Dirichlet condition is given on one side of the cut and Neumann condition is specified on the other side. Basing on the method of potentials the problem is reduced to the uniquely solvable Fredholm integral equation of the second kind. The behavior of a solution gradient at the tips of the cut is studied.