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We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[1,∞) is bounded away from 1 and ∞. We discuss the relation between the Hausdorff dimension and the Sobolev capacity. As another application we study quasicontinuous representatives in the space W1, p(⋅)(ℝn)

journal of function spaces and applications/journal of function spaces and applications

Sobolev capacity on the space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mrow><mml:mo>⋅</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:…

Sobolev capacity on the spaceW1, p(⋅)(ℝn)