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Τι (ποιος) είναι R James Milgram - ορισμός

THEOREM

Lax-Milgram theorem; Lax–Milgram theorem; Lax-Milgram lemma; Lax–Milgram lemma

R. James Milgram

AMERICAN MATHEMATICIAN

Richard James Milgram (born 5 December 1939 in South Bend, Indiana) is an American mathematician, specializing in algebraic topology. He is the son of mathematician Arthur Milgram.

https://en.wikipedia.org/wiki/R._James_Milgram

Arthur Milgram

AMERICAN MATHEMATICIAN

Milgram, Arthur

Arthur Norton Milgram (3 June 1912, in Philadelphia – 30 January 1961) was an American mathematician. He made contributions in functional analysis, combinatorics, differential geometry, topology, partial differential equations, and Galois theory.

https://en.wikipedia.org/wiki/Arthur_Milgram

Lions–Lax–Milgram theorem

A RESULT IN FUNCTIONAL ANALYSIS WITH APPLICATIONS IN THE STUDY OF PARTIAL DIFFERENTIAL EQUATIONS

Lions-Lax-Milgram theorem; Lions theorem; Lions' theorem; Lions’ theorem; Lions's theorem

In mathematics, the Lions–Lax–Milgram theorem (or simply Lions's theorem) is a result in functional analysis with applications in the study of partial differential equations. It is a generalization of the famous Lax–Milgram theorem, which gives conditions under which a bilinear function can be "inverted" to show the existence and uniqueness of a weak solution to a given boundary value problem.

https://en.wikipedia.org/wiki/Lions–Lax–Milgram_theorem

Βικιπαίδεια

Weak formulation

Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.

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.

https://en.wikipedia.org/wiki/Weak formulation