A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators
We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
Analytical solution of a general boundary value problem for a BKW-equation.