Properties of solutions of a class of planar elliptic operators with degeneracies.

In this paper we investigate properties of solutions of first and second order elliptic equations that degenerate along a simple closed curve in $ \mathbb{R}^2$ $ \mathbb{C}$. To the vector field $ L$ $ \mathbb{P}=\mathrm{Re}\left[L\overline{L} L \right]$ is a $ \mathbb{C}$ $ \mathbb{P}u=0$ $ Lw=Aw\overline{w}$ [ABSTRACT FROM AUTHOR]