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In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross , who established them in dimension-independent form, [ 1 ] [ 2 ] in the context of constructive quantum field theory .
The Sobolev embedding theorem holds for Sobolev spaces W k,p (M) on other suitable domains M. In particular (Aubin 1982, Chapter 2; Aubin 1976), both parts of the Sobolev embedding hold when M is a bounded open set in R n with Lipschitz boundary (or whose boundary satisfies the cone condition; Adams 1975, Theorem 5.4) M is a compact Riemannian ...
In mathematics, the Poincaré inequality [1] is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré.The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition.
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of L p-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete , i.e. a Banach space .
Here log + is the positive part of the logarithm. Also included in the class of Orlicz spaces are many of the most important Sobolev spaces. In addition, the Orlicz sequence spaces are examples of Orlicz spaces.
Buzz around NFL free agency will pick up as Super Bowl 59 comes and goes. Here's what to know about the top available players on the open market.
The world's largest memory chip, smartphone and TV maker expects to log an operating profit of 6.5 trillion won ($4.5 billion) for the three months ended Dec. Samsung's preliminary Q4 profit falls ...
Prof Sergei Lvovich Sobolev, FRSE (Russian: Серге́й Льво́вич Со́болев; 6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations.