Poincaré-Friedrichs Inequalities

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.