Symmetric gradient Sobolev spaces endowed with rearrangement-invariant norms

A unified approach to embedding theorems for Sobolev type spaces of vector-valued functions, defined via their symmetric gradient, is proposed. The in question are built upon general rearrangement-invariant norms. Optimal target the relevant embeddings determined within class all spaces. In particular, gradient into shown be equivalent corresponding full same sharp condition uniformly continuous and optimal targets, also exhibited. By contrast, these may weaker than ones gradient. Related results, independent interest theory spaces, established. They include global approximation extension under minimal assumptions on domain. formula K-functional, which pivotal our method based reduction one-dimensional inequalities, provided as well. case Orlicz-Sobolev use mathematical models continuum mechanics driven by nonlinearities non-power type, especially focused.