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Oblique derivative

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directional derivative

A derivative of a function defined in a neighbourhood of the points of some surface , with respect to a direction different from the direction of the conormal of some elliptic operator at the points of . Oblique derivatives may figure in the boundary conditions of boundary value problems for second-order elliptic equations. The problem is then called a problem with oblique derivative. See Differential equation, partial, oblique derivatives.

If the direction field on has the form , where are functions of the points such that , then the oblique derivative of a function with respect to is

where are Cartesian coordinates in the Euclidean space .

References

[1] C. Miranda, "Partial differential equations of elliptic type" , Springer (1970) (Translated from Italian)
How to Cite This Entry:
Oblique derivative. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Oblique_derivative&oldid=12774
This article was adapted from an original article by A.I. Yanushauskas (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article