Titlebook: Sobolev Spaces in Mathematics I; Sobolev Type Inequal Vladimir Maz’ya Book 2009 Springer-Verlag New York 2009 Sobolev inequlaity.Sobolev i

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My Love Affair with the Sobolev Inequality,Reminiscence about different versions of the Sobolev inequality obtained by the author and others.

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,On the Hardy–Sobolev–Maz’ya Inequality and Its Generalizations,Abstract The paper deals with natural generalizations of the Hardy— Sobolev—Maz‘ya inequality and some related questions, such as the optimality and stability of such inequalities, the existence of minimizers of the associated variational problem, and the natural energy space associated with the given functional.

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Sobolev Inequalities in Familiar and Unfamiliar Settings,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.

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