@article{HarutyunyanSchulze2006,
  author    = {Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem with singular interfaces as a corner boundary value problem},
  series = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis},
  volume    = {25},
  journal   = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0926-2601},
  doi       = {10.1007/s11118-006-9020-6},
  pages     = {327 -- 369},
  year      = {2006},
  abstract  = {We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.},
  language  = {en}
}