Abstract
<abstract><p>Let $ \Omega $ be an exterior Lipschitz domain in $ \mathbb{R}^2 $. It is proved that the Helmholtz decomposition of the vector fields in $ L_p (\Omega; \mathbb{R}^2) $ exists if $ p $ satisfies $ \lvert1/ p - 1/ 2 \rvert < 1/ 4+ \varepsilon $ with some constant $ \varepsilon = \varepsilon (\Omega) \in (0, 1/ 4] $, where it is allowed to take $ \varepsilon = 1/ 4 $ if $ \partial \Omega \in C^1 $.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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