Green line

An orthogonal trajectory of a family of level surfaces $G_y(x)=r$, $0\leq r<+\infty$, where $G_y(x)=G(x,y)$ is the Green function (of the Dirichlet problem for the Laplace equation) for a domain $D$ in a Euclidean space $\mathbf R^n$, $n\geq2$, with a given pole $y\in D$. In other words, Green lines are integral curves in the gradient field $\operatorname{grad}G_y(x)$. Generalizations also exist [2].

#### References[edit]

[1] |  N.S. [N.S. Landkov] Landkof, "Foundations of modern potential theory" , Springer (1972) pp. Chapt. 1 (Translated from Russian)

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[2] |  M. Brélot, G. Choquet, "Espaces et lignes de Green" Ann. Inst. Fourier , 3 (1952) pp. 199–263