The Lax-Milgram Theorem, named after Peter Lax and Arthur Milgram, who proved it in 1954, provides weak formulations for certain systems of equations posed on Hilbert spaces, the setting in which a solution is required to satisfy the equation only against a suitable space of test functions rather than in the strong, pointwise sense assumed by the original formulation. Weak formulations built this way carry many linear-algebra techniques over to the study of partial differential equations, and the Lax-Milgram Theorem supplies the essential existence and uniqueness guarantee that makes such weak solutions well defined.
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Statement Form Statement Form Statement Form StatementIf a is a bounded and coercive bilinear form on a Hilbert space V, then for any bounded f in V', there is a unique solution u in V to the equation a(u,v) = f(v) for all v in V. 1 Connections
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Source Arthur Milgram (Wikipedia)
Sources
1. Lax-Milgram theorem (Wikipedia)
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The Lax-Milgram theorem, named after Peter Lax and Arthur Milgram who proved it in 1954, provides weak formulations for certain systems on Hilbert spaces.
General concept
named after Peter Lax and Arthur Milgram who proved it in 1954
View the SourceArthur Milgram (Wikipedia)
Principal Result Of: Arthur Milgram, Lead, principal resultQuote, Principal Result Of: Arthur Milgram, Lead, principal result
Perhaps one of his more famous contributions is the Lax-Milgram theorem
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