Zeit und Ort

Dienstag, 9.6.26, 14:15–15:15, Seminarraum 226, HH10

Zusammenfassung

We establish a pointwise limit theorem for a broad class of parameter-dependent BMO-type seminorms as the parameter tends to zero. By introducing novel BMO-type seminorms, we provide a unified framework that extends several existing results and yields non-distributional characterizations of Sobolev-type spaces, both in the scalar and in the vector-valued setting. More precisely, for any open set \(\Omega\subset \mathbb{R}^n\) and any \(p\in (1, \infty)\), we provide a characterization of the Sobolev space \(W^{1,p}(\Omega; \mathbb{R}^m)\). In addition, we characterize the space \(E^{1,p}(\Omega;\mathbb{R}^n)\) of \(L^p\) maps with \(p\)-integrable distributional symmetric gradient. Finally, for all \(p\in [1, \infty)\), we show that these seminorms converge to integral functionals with convex, \(p\)-homogeneous integrands associated with the distributional gradient and the symmetric gradient.