×

zbMATH — the first resource for mathematics

A refinement of Rellich’s theorem. (English) Zbl 0666.46041
If \(u_ k\) converges weakly to u in the Sobolev space \(H_ 0^{1,p}(U)\), \(U\subset {\mathbb{R}}^ n\), \(1\leq p\leq n\), then the exceptional sets \(E_ k=\{x\in U:\) \(| u_ k-u| \geq \epsilon \}\) are analysed. Their relative capacities are shown to vanish in a weak sense, which leads to new compactness results for solutions of certain elliptic inequalities.
Reviewer: J.F.Toland

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
PDF BibTeX XML Cite