Displaying similar documents to “Poincaré inequalities and Sobolev spaces.”

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].

Subelliptic Poincaré inequalities: the case p < 1.

Stephen M. Buckley, Pekka Koskela, Guozhen Lu (1995)

Publicacions Matemàtiques

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We obtain (weighted) Poincaré type inequalities for vector fields satisfying the Hörmander condition for p < 1 under some assumptions on the subelliptic gradient of the function. Such inequalities hold on Boman domains associated with the underlying Carnot- Carathéodory metric. In particular, they remain true for solutions to certain classes of subelliptic equations. Our results complement the earlier results in these directions for p ≥ 1.

Sobolev spaces on multiple cones

P. Auscher, N. Badr (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from ℝ n . The analysis interestingly combines use of Poincaré inequalities and of some Hardy type inequalities.

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 .