In functional analysis, the term "Poincaré-Friedrichs inequality" is a term used to describe inequalities which are qualitatively similar to the classical Poincaré Inequality and/or Friedrichs inequalities. Sometimes referred to as inequalities of Poincaré-Friedrichs type, such expressions play important roles in the theories of partial differential equations and function spaces, often implying relationships between functions in L-p and Sobolev spaces that would be otherwise-difficult to conclude.
Poincaré-Friedrichs Inequalities
See also
Friedrichs Inequality, Function Space, L-p-Space, Poincaré Inequality, Sobolev SpaceThis entry contributed by Christopher Stover
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References
Vohralík, M. "On the Discrete Poincaré-Friedrichs Inequalities for Nonconforming Approximations to the Sobolev Space ." Numer. Func. Anal. Opt. 26, 925-952, 2005.Zheng, W. "On Friedrichs-Poincaré-Type Inequalities." J. Math. Anal. Appl. 304, 542-551, 2005.Cite this as:
Stover, Christopher. "Poincaré-Friedrichs Inequalities." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Poincare-FriedrichsInequalities.html