TY  - JOUR
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem with singular interfaces as a corner boundary value problem
JF  - Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis
N2  - 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.
KW  - Zaremba problem
KW  - corner Sobolev spaces with double weights
KW  - pseudo-differential boundary value problems
Y1  - 2006
U6  - https://doi.org/10.1007/s11118-006-9020-6
SN  - 0926-2601
VL  - 25
SP  - 327
EP  - 369
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - INPR
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem with singular interfaces as a corner boundary value problem
N2  - 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 ⊂ 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 [3]. 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.
T3  - Preprint - (2004) 26 
KW  - Zaremba problem
KW  - corner Sobolev spaces with double weights
KW  - pseudodifferential boundary value problems
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26855
ER  -