Decompositions of the Sobolev–Clifford Modules and Nonlinear Variational Problems

We establish a general direct decomposition of modules and then, using this decomposition, prove representations of the Sobolev–Clifford modules as the sums of submodules of monogenic and comonogenic functions. We also show how the decompositions obtained can be applied to solving Stokes-type nonlinear variational problems.