Unimproved estimations in Hoelder space for generalized solutions of a biharmonic equation, a system of Navier-Stokes equations, and Karman systems in nonsmooth two-dimensional regions

For solutions to the homogeneous Dirichlet problem for the biharmonic equation with the right part consisting of Lp(Omega), a Karman system, and a system of Navier-Stokes equations in a two-dimensional region, it is proven that their first derivatives satisfy the Holder condition with an exponent dependent on the geometric structure of the region. This exponent is also the root of a specified transcendental equation and is unimproved in a class of regions with a corresponding geometric structure.