An invitation to Korn-type inequalities

This mini course is tailored to PhD students and postdocs, but everyone who is interested is welcome to attend.

Inequalities of Korn-type bound norms of differential expressions by parts thereof. Such inequalities and their generalisations display instrumental tools in the well-posedness theory for problems from nonlinear elasticity or fluid mechanics, making them an important subject beyond theoretical interest.
The minicourse offers an introduction to such inequalities, ranging from basic material to recent directions. Here, a special emphasis is put on the different forms of Korn-type inequalities, the underlying approaches and their natural limitations. Eventually, we will embed the theme of Korn-type inequalities into the so-called incompatible framework. This will bring us to the recently obtained classification within Korn-Maxwell-Sobolev inequalities.