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Difference between revisions of "Gårding inequality"

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Revision as of 18:52, 24 March 2012

An inequality of the form

where is a complex-valued function with compact support (in ), is a bounded domain and

is a quadratic integral form with complex continuous coefficients in . A sufficient condition for the Gårding inequality to be valid for any function is the existence of a positive constant such that

for any and all real vectors . Formulated and proved by L. Gårding [1].

References

[1] L. Gårding, "Dirichlet's problem for linear elliptic partial differential equations" Math. Scand. , 1 (1953) pp. 55–72
[2] K. Yosida, "Functional analysis" , Springer (1980) pp. Chapt. 8, §1


Comments

A sharp form of this inequality has been given by L. Hörmander. See [a1], Sects. 18.1, 18.6, and the literature quoted there.

References

[a1] L.V. Hörmander, "The analysis of linear partial differential operators" , 3 , Springer (1985)
How to Cite This Entry:
Gårding inequality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=G%C3%A5rding_inequality&oldid=22479
This article was adapted from an original article by A.A. Dezin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article