Displaying similar documents to “Sobolev spaces on multiple cones”

Poincaré inequalities and Sobolev spaces.

Paul MacManus (2002)

Publicacions Matemàtiques

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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. ...

Nonlinear Maps between Besov and Sobolev spaces

Philip Brenner, Peter Kumlin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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Our main result shows that for a large class of nonlinear local mappings between Besov and Sobolev space, interpolation is an exceptional low dimensional phenomenon. This extends previous results by Kumlin [13] from the case of analytic mappings to Lipschitz and Hölder continuous maps (Corollaries 1 and 2), and which go back to ideas of the late B.E.J. Dahlberg [8].

Hölder quasicontinuity of Sobolev functions on metric spaces.

Piotr Hajlasz, Juha Kinnunen (1998)

Revista Matemática Iberoamericana

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We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Malý [Ma1] to the Sobolev spaces on metric spaces [H1].

Relative rearrangement and interpolation inequalities.

J. Michel Rakotoson (2003)

RACSAM

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We prove here that the Poincaré-Sobolev pointwise inequalities for the relative rearrangement can be considered as the root of a great number of inequalities in various sets not necessarily vector spaces. In particular, new interpolation inequalities can be derived.

Definitions of Sobolev classes on metric spaces

Bruno Franchi, Piotr Hajłasz, Pekka Koskela (1999)

Annales de l'institut Fourier

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There have been recent attempts to develop the theory of Sobolev spaces W 1 , p on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We also define the spaces in the limiting case p = 1 .