Title: A local-to-global method for inequalities in weighted Sobolev spaces.

Abstract: In this talk, we will discuss a certain local-to-global technique with applications to inequalities in weighted Sobolev spaces, such as fractional Poincaré-type inequalities and Korn and conformal Korn inequalities. This technique is based on a certain decomposition of functions that extends the validity of the inequalities from cubes or regular domains to more general Euclidean domains, including John domains and Holder-domains, and weighted spaces. Some estimations of the optimal constants are also obtained.