The skew derivative problem in the exterior of open curves in a plane
In several preceding papers, the author considered the Dirichlet and Neumann problems for the Helmholtz equation outside cuts in the plane [cf. Comput. Math. Math. Phys. 34, 1073--1090 and 1421--1431 (1994; Zbl 0835.35033 and Zbl 0835.35034)]. Utilizing related ideas, in the present paper the skew derivative problem for the two-dimensional Laplace equation is investigated in the exterior of open curves. The essential step is the reduction of the problem to a Fredholm integral equation of the second kind. Results on the existence, uniqueness, regularity and construction of solutions are obtained.
scientific article; zbMATH DE number 1068009
scientific article