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Variable exponent trace spaces

100%

Diening L., Hästö P.

Studia Mathematica

2007

tom 183

nr 2

127-141

The trace space of $W^{1,p(·)}(ℝⁿ × [0,∞))$ consists of those functions on ℝⁿ that can be extended to functions of $W^{1,p(·)}(ℝⁿ × [0,∞))$ (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

81%

Harjulehto P., Hästö P., Koskenoja M., Varonen S.

Banach Center Publications

2005

tom 68

nr 1

51-59

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.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Hästö P.

1 Diening L.

1 Harjulehto P.

1 Koskenoja M.

1 Varonen S.

1 2007

1 2005

Wyniki wyszukiwania

Variable exponent trace spaces

Variable Sobolev capacity and the assumptions on the exponent