Variable exponent Sobolev spaces with zero boundary values
We study different definitions of the first order variable exponent Sobolev space with zero boundary values in an open subset of .
A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.
We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e.g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.
Differentiation bases for Sobolev functions on metric spaces.
We study Lebesgue points for Sobolev functions over other collections of sets than balls. Our main result gives several conditions for a differentiation basis, which characterize the existence of Lebesgue points outside a set of capacity zero.
Uniform convexity and associate spaces
We prove that the associate space of a generalized Orlicz space is given by the conjugate modular even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling -function is equivalent to a doubling -function. As a consequence, we conclude that is uniformly convex if and are weakly doubling.
Maximal inequality in -uniform domains.
Variable Sobolev capacity and the assumptions on the exponent
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.
Fine topology of variable exponent energy superminimizers.
Lebesgue points in variable exponent spaces.
Unbounded supersolutions of nonlinear equations with nonstandard growth.
Hölder quasicontinuity in variable exponent Sobolev spaces.
Fuglede's theorem in variable exponent Sobolev space.
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