engleski

Maximally singular Sobolev functions

We construct a class of maximally singular Sobolev functions, that is, such that the Hausdorff dimension of their singular set is equal to $N-mp$. The result has been announced by the second author in [Chaos Solitons Fractals 21 (2004), p. 1287]. The precise values of lower and upper Minkowski contents of Sierpinski carpet are computed and applied to the study of asymptotics of some singular integrals.

Sobolev function; Bessel potential; fractal set; Minkowski content; Sierpinski carpet

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