Variable Besov and Triebel--Lizorkin spaces.
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 .
Variable exponent trace spaces
The trace space of consists of those functions on ℝⁿ that can be extended to functions of (as in the fixed-exponent case). Under the assumption that p is globally log-Hölder continuous, we show that the trace space depends only on the values of p on the boundary. In our main result we show how to define an intrinsic norm for the trace space in terms of a sharp-type operator.
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.
Variational fractals
Variational inequalities for energy functionals with nonstandard growth conditions.
Variational inequalities of strongly nonlinear elliptic operators of infinite order.
Variational inequalities of strongly nonlinear elliptic operators of infinite order.
Vector-valued Morrey's embedding theorem and Hölder continuity in parabolic problems.