Browder-Minty theorem

Browder-Minty theorem

In mathematics, the Browder-Minty theorem states that a bounded, continuous, coercive and monotone function "T" from a real, reflexive Banach space "X" into its continuous dual space "X"∗ is automatically surjective. That is, for each continuous linear functional "g" ∈ "X"∗, there exists a solution "u" ∈ "X" of the equation "T"("u") = "g". (Note that "T" itself is not required to be a linear map.)

ee also

* Pseudo-monotone operator; pseudo-monotone operators obey a near-exact analogue of the Browder-Minty theorem.

References

* cite book
author = Renardy, Michael and Rogers, Robert C.
title = An introduction to partial differential equations
series = Texts in Applied Mathematics 13
edition = Second edition
publisher = Springer-Verlag
location = New York
year = 2004
pages = 361
id = ISBN 0-387-00444-0 (Theorem 9.45)


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