Difference between revisions of "Green line"
From Encyclopedia of Mathematics
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| − | An orthogonal trajectory of a family of level surfaces | + | {{TEX|done}} |
| + | 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|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 [[#References|[2]]]. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> N.S. [N.S. Landkov] Landkof, "Foundations of modern potential theory" , Springer (1972) pp. Chapt. 1 (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> M. Brélot, G. Choquet, "Espaces et lignes de Green" ''Ann. Inst. Fourier'' , '''3''' (1952) pp. 199–263</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> N.S. [N.S. Landkov] Landkof, "Foundations of modern potential theory" , Springer (1972) pp. Chapt. 1 (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> M. Brélot, G. Choquet, "Espaces et lignes de Green" ''Ann. Inst. Fourier'' , '''3''' (1952) pp. 199–263</TD></TR></table> | ||
Latest revision as of 13:59, 1 October 2014
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
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