This paper is concerned with jump conditions for the double layer potential associated with the two-dimensional Helmholtz equation for Hölder continuous boundary data on arbitrary rectifiable Jordan closed curves in ℝ².
In this note we establish a necessary and sufficient condition for solvability of the homogeneous Riemann boundary problem with infinity index on a rectifiable open curve. The index of the problem we deal with considers the influence of the requirement of the solutions of the problem, the degree of non-smoothness of the curve at the endpoints as well as the behavior of the coefficient at these points.
In this note, based on a natural isomorphism between the spaces of differential forms and Clifford algebra-valued multi-vector functions, the Cauchy type integral for self-conjugate differential forms in ℝⁿ is considered.
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