Some problems of vector analysis in solenoidal spaces
In the first part of the paper we study some properties of eigenelements of linear selfadjoint pencils Lu = λBu. In the second part we apply these results to the investigation of some boundary value problems for mixed type second order operator-differential equations.
We reformulate and extend G. Nguetseng’s notion of two-scale convergence by means of a variable transformation, and outline some of its properties. We approximate two-scale derivatives, and extend this convergence to spaces of differentiable functions. The two-scale limit of derivatives of bounded sequences in the Sobolev spaces , , and is then characterized. The two-scale limit behaviour of the potentials of a two-scale convergent sequence of irrotational fields is finally studied.