Unimproved estimations in Hoelder space for generalized solutions of a biharmonic equation, a system of NavierStokes equations, and Karman systems in nonsmooth twodimensional regions
Abstract
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 NavierStokes equations in a twodimensional 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.
 Publication:

Moskovskii Universitet Vestnik Seriia Matematika Mekhanika
 Pub Date:
 December 1983
 Bibcode:
 1983MVSMM.......22K
 Keywords:

 Biharmonic Equations;
 Dirichlet Problem;
 Flow Geometry;
 NavierStokes Equation;
 Two Dimensional Flow;
 Von Karman Equation;
 Flow Equations;
 Function Space;
 Transcendental Functions;
 Fluid Mechanics and Heat Transfer