Displaying similar documents to “Weighted Sobolev spaces and capacity.”

Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

Banach Center Publications

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In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.

On imbedding theorems for weighted anisotropic Sobolev spaces

Wojciech M. Zajączkowski (2002)

Applicationes Mathematicae

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Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.

General Gagliardo Inequality and Applications to Weighted Sobolev Spaces

Antonio Avantaggiati, Paola Loreti (2009)

Bollettino dell'Unione Matematica Italiana

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In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].

Dimension-invariant Sobolev imbeddings

Miroslav Krbec, Hans-Jürgen Schmeisser (2011)

Banach Center Publications

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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.