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Conormal

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A term used in the theory of boundary value problems for partial differential equations (cf. Boundary value problem, partial differential equations). Let be the outward normal at a point to a smooth surface situated in a Euclidean space with coordinates , and let be a contravariant continuous tensor, usually representing the coefficients of some second-order (elliptic) differential operator . Then the conormal (with respect to ) is the vector

where . In other words, the conormal is the contravariant description (in the space with metric defined by the tensor inverse to ) of the normal covariant vector to (in the space with Euclidean metric).

References

[1] A.V. Bitsadze, "Equations of mathematical physics" , MIR (1980) (Translated from Russian)
[2] C. Miranda, "Partial differential equations of elliptic type" , Springer (1970) (Translated from Italian)


Comments

References

[a1] A. Friedman, "Partial differential equations of parabolic type" , Prentice-Hall (1964)
How to Cite This Entry:
Conormal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conormal&oldid=46480
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article