Singularities of solutions to linear, second order, analytic elliptic equations in two independent variables. II

Abstract

The analysis of Part I is extended to admit of a closed boundary composed of intersecting analytic arcs. The boundary data have branch point singularities for values of the arclength parameter corresponding to intersections of the boundary arcs. These singularities are associated with nonuniformity of the solution to the boundary value problem at the intersections. Complex characteristics and the generalized Huygens principle are used to relate singularities of the data to those of the solution. By way of illustration, the analytic continuation of the boundary data is performed for the Laplace equation whose solution satisfies a simple Neumann condition on a boundary consisting of a semicircle and its diameter