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An orthogonal trajectory of a family of level surfaces , , where is the Green function (of the Dirichlet problem for the Laplace equation) for a domain in a Euclidean space , , with a given pole . In other words, Green lines are integral curves in the gradient field . 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=33454
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article