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.
Facts
Classification
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
Sources
1. Lax-Milgram theorem (Wikipedia)
The Lax-Milgram theorem
there is a unique solution u Γêê V to the equation
General concept
named after Peter Lax and Arthur Milgram who proved it in 1954
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