Estimating ∇u in terms of divu, curlu, either (ν,u) or ν×u and the topology
Jürgen Bolik, Wolf von Wahl · Mathematical Methods in the Applied Sciences · 1997
In the present paper we prove Cα-estimates for ∇u using components of boundary values of u, div u, curl u and quantities given by components of boundary values of u as well as boundary values of elements belonging to de Rhams cohomology modules. The vector field u is defined on a bounded set G¯⊂ℝ3, meanwhile the cohomology group will be defined with regard to ℝ3−G. Our inequalities turn out to be a priori estimates concerning well-known boundary value problems for vector fields. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.