Constructions of bounded solutions of $div\mathbf{u}=f$ in critical spaces

Albert Cohen, Ronald DeVore, Eitan Tadmor

We construct uniformly bounded solutions of the equation $div\mathbf{u}=f$ for arbitrary data $f$ in the critical spaces $L^d(\hat{I}\text{c◯})$, where $\hat{I}\text{c◯}$ is a domain of ${\mathbb{R}}^d$. T…