Classical solutions of two‐dimensional stokes problems on non‐smooth domains. Part 1: The radon integral operators
Jean M.-S. Lubuma · Mathematical Methods in the Applied Sciences · 1993
Abstract The applicability of the Neumann indirect method of potentials to the Dirichlet and Neumann problems for the two‐dimensional Stokes operator on a non‐smooth boundary Γ is subject to two kinds of sufficient and/or necessary conditions on Γ. The first one, occurring in electrostatic, is equivalent to the boundedness onC(Γ) of the velocity double‐layer potentialWas well as to the existence of jump relations of potentials. The second condition, which forces Γ to be a simple rectifiable curve and which, compared to the Laplacian, is a stronger restriction on the corners of Γ, states that the Fredholm radius ofWis greater than 2. Under these conditions, the Radon boundary integral equations defined by the above‐mentioned jump relations are solvable by the Fredholm theory; the double‐ (for Dirichlet) and the single‐ (for Neumann) layer potentials corresponding to their solutions are classical solutions of the Stokes problems.