Chapter

Sobolev Spaces In Mathematics I

Volume 8 of the series International Mathematical Series pp 299-343

Sobolev Inequalities in Familiar and Unfamiliar Settings

  • Laurent Saloff-CosteAffiliated withCornell University, Mallot Hall

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Abstract

The classical Sobolev inequalities play a key role in analysis in Euclidean spaces and in the study of solutions of partial differential equations. In fact, they are extremely flexible tools and are useful in many different settings. This paper gives a glimpse of assortments of such applications in a variety of contexts.