Oblique derivative
From Encyclopedia of Mathematics
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=32599
Oblique derivative. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Oblique_derivative&oldid=32599
This article was adapted from an original article by A.I. Yanushauskas (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article