Namespaces
Variants
Actions

Green line

From Encyclopedia of Mathematics
Revision as of 13:59, 1 October 2014 by Ivan (talk | contribs) (TeX)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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

[1] N.S. [N.S. Landkov] Landkof, "Foundations of modern potential theory" , Springer (1972) pp. Chapt. 1 (Translated from Russian)
[2] M. Brélot, G. Choquet, "Espaces et lignes de Green" Ann. Inst. Fourier , 3 (1952) pp. 199–263
How to Cite This Entry:
Green line. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Green_line&oldid=15952
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article