Abstract
The term “Poincaré type inequality” is used, somewhat loosely, to describe a class of inequalities that generalize the classical Poincaré inequality,
valid for f ∈ W 1,p0 (Ω) in a bounded open Ω ⊂ RN. What the inequalities have in common is that an integral norm of a function is estimated in terms of integrals of its derivatives, and some information about the vanishing or the average of the function. Some such knowledge is clearly necessary, since estimates of this kind are false for non-zero constants.
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© 1996 Springer-Verlag Berlin Heidelberg
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Adams, D.R., Hedberg, L.I. (1996). Poincaré Type Inequalities. In: Function Spaces and Potential Theory. Grundlehren der mathematischen Wissenschaften, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03282-4_8
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DOI: https://doi.org/10.1007/978-3-662-03282-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08172-9
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