On the Regularity of the Principle Value of the Double Layer Potential

摘要

The regularity of the principal value of the potential due to a doublet distribution mu along the boundary S of a two-dimensional (2-D) open connected set is discussed. Assuming S to be a Lyapunov boundary and mu to be bounded and integrable it is proved that the principal value in 2-D is more regular than the one in 3-D. This result is applied to the aerodynamic problem of calculation of potential flows around 2-D bodies.