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 $L^d(\Omega )$, where $\Omega$ is a domain of ${\mathbb{R}}^d$. Thi…