We review the proof of existence and uniqueness of the Poisson's equation $\Delta u=div m=0$ whenever $m$ is a unit $L^2$ vector field on $R^3$ with compact support. By standard linear potential theory we deduce also $H^1$ regularity of the unique weak solution.
|Number of pages||4|
|Journal||DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S|
|Publication status||Published - 2015|
- Poisson equation
- Riesz potential