Displaying similar documents to “Variable exponent Sobolev spaces with zero boundary values”

Non-Newtonian fluids and function spaces

Růžička, Michael, Diening, Lars

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In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted N -functions that are used in the studies of generalized Newtonian fluids and problems with p -structure.

Recent developments in the theory of function spaces with dominating mixed smoothness

Schmeisser, Hans-Jürgen

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The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...

Coarea integration in metric spaces

Malý, Jan

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Let X be a metric space with a doubling measure, Y be a boundedly compact metric space and u : X → Y be a Lebesgue precise mapping whose upper gradient g belongs to the Lorentz space L m , 1 , m ≥ 1 . Let E ⊂ X be a set of measure zero. Then ℋ ^ m ( E ∩ u - 1 ( y ) ) = 0 for ℋ m -a.e. y ∈ Y , where ℋ m is the m -dimensional Hausdorff measure and ℋ ^ m is the m -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of...