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On the equations rot v$$=g$$ and div u$$=f$$ with zero boundary conditions. (English) Zbl 0719.35014
The authors study the equations rot v$$=g$$ and div u$$=f$$ in both bounded and exterior domains under homogeneous Dirichlet data. They give necessary and sufficient conditions for existence of solutions in Sobolev spaces and investigate in particular higher regularity of the solutions. Various results for the equations that are studied here are well known, and different methods have been used to prove them. The present paper presents a complete description of the results together with clear proofs.

##### MSC:
 35F15 Boundary value problems for linear first-order PDEs 35Q30 Navier-Stokes equations 35B65 Smoothness and regularity of solutions to PDEs
##### Keywords:
exterior domains; Dirichlet data; higher regularity
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