Maximally singular Sobolev functions
In any Sobolev space \(W^{m,p}(\mathbb{R}^N)\) with \(p>1\), \(mp\leq N\), a function is constructed, the set of singular points of which has the maximal possible Hausdorff dimension equal to \(N-mp\). The analogous result is proven also for Bessel potential spaces \(L^{\alpha,p}(\mathbb{R})\) with \(\alpha>0\), \(p>1\).
scientific article; zbMATH DE number 2157698