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Seminar on theory of function spaces

Optimal Sobolev embeddings for symmetric gradients (joint work with Andrea Cianchi)

Dominic Breit
Heriot-Watt University, Edinburgh


Thursday, 22. October 2020 - 15:40 to 17:40

On-line seminar; for the access data write to Luboš Pick

I will present an unified approach to embedding theorems for Sobolev type spaces of vector-valued functions, defined via their symmetric gradient. The Sobolev spaces in question are built upon general rearrangement-invariant norms. Optimal target spaces in the relevant embeddings are determined within the class of all rearrangement-invariant spaces. In particular, I show that all symmetric gradient Sobolev embeddings into rearrangement-invariant target spaces are equivalent to the corresponding embeddings for the full gradient built upon the same spaces.