Poincaré-Friedrichs inequalities in functional analysis are 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 Lp and Sobolev spaces that would be otherwise difficult to conclude (Zheng and Qi 2005, pp. 542-543).
Poincaré-Friedrichs Inequalities
See also
Friedrichs Inequality, Function Space, Lp-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 of the Sobolev Space
." Numer. Funct. Anal. Optim. 26, 925-952,
2005. https://doi.org/10.1080/01630560500444533.Zheng,
W. and Qi, H. "On Friedrichs-Poincaré-Type Inequalities." J.
Math. Anal. Appl. 304, 542-551, 2005. https://doi.org/10.1016/j.jmaa.2004.09.066.Referenced on Wolfram|Alpha
Poincaré-Friedrichs InequalitiesCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Poincaré-Friedrichs Inequalities." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Poincare-FriedrichsInequalities.html