An estimate in the spirit of Poincaré's inequality

Augusto C. Ponce

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Displaying similar documents to “An estimate in the spirit of Poincaré's inequality”

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We define a Sobolev space by means of a generalized Poincaré inequality and relate it to a corresponding space based on upper gradients.

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We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.

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Our understanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function. ...

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