Browder-Minty theorem
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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.)
[edit] See also
- Pseudo-monotone operator; pseudo-monotone operators obey a near-exact analogue of the Browder-Minty theorem.
[edit] References
- Renardy, Michael and Rogers, Robert C. (2004). An introduction to partial differential equations, Second edition, Texts in Applied Mathematics 13, New York: Springer-Verlag, 361. ISBN 0-387-00444-0. (Theorem 9.45)
