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.
Lussardi, L., On a Poisson's equation arising from magnetism, <<DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S>>, 2015; 8 (4): 769-772. [doi:10.3934/dcdss.2015.8.769] [http://hdl.handle.net/10807/64694]
On a Poisson's equation arising from magnetism
Lussardi, Luca
2015
Abstract
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.
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