On some transmission problems in a plane corner. (English) Zbl 1474.35709
Summary: We consider the transmission problem in Sobolev-Slobodetskii spaces for two model general elliptic pseudodifferential equations in a plane, where one equation is given inside a corner, and another one is outside. Starting from general solutions of these equations we consider certain transmission conditions on angle sides. For some cases this transmission problem was reduced to an equivalent system of one-dimensional linear integral equations.
MSC:
35S15 | Boundary value problems for PDEs with pseudodifferential operators |
47G40 | Potential operators |