## View abstract

### Invited talk

Monday, July 19, 13:30 ~ 14:30 UTC-3

## Solutions of the divergence, decomposition of $L^p$-functions, and applications.

### Ricardo Durán

The Lions lemma is equivalent to the existence of appropriate solutions of the equation $div\,u=f$. In this talk we recall how solutions of the divergence equation can be constructed by elementary arguments in a very general class of bounded domains. Then, we show how these solutions can be used to obtain a decomposition of a function of vanishing integral in a domain into a sum of locally supported functions with the same property.