Document Type

Article

Publication Date

2016

Department

Mathematics

Abstract

We prove an inequality that resembles Cacciopoli inequalities in that it bounds the norm of the derivative of a function by using the norm of the function. Unlike in Cacciopoli inequalities, there is no restriction on the function, a fact made up for by adding an extra term to the norm of the function. The inequality arose in the proof that a bilinear form associated with spatial hysteresis internal damping for an Euler-Bernoulli beam is coercive.

Publication Title

Journal of Mathematical Analysis and Applications

Volume

425

Issue

1

First Page

520

Last Page

535

Included in

Mathematics Commons

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