@unpublished{GrudskyTarkhanov2012,
  author    = {Grudsky, Serguey and Tarkhanov, Nikolai Nikolaevich},
  title     = {Conformal reduction of boundary problems for harmonic functions in a plane domain with strong singularities on the boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57745},
  year      = {2012},
  abstract  = {We consider the Dirichlet, Neumann and Zaremba problems for harmonic functions in a bounded plane domain with nonsmooth boundary. The boundary curve belongs to one of the following three classes: sectorial curves, logarithmic spirals and spirals of power type. To study the problem we apply a familiar method of Vekua-Muskhelishvili which consists in using a conformal mapping of the unit disk onto the domain to pull back the problem to a boundary problem for harmonic functions in the disk. This latter is reduced in turn to a Toeplitz operator equation on the unit circle with symbol bearing discontinuities of second kind. We develop a constructive invertibility theory for Toeplitz operators and thus derive solvability conditions as well as explicit formulas for solutions.},
  language  = {en}
}