Maximally singular Sobolev functions
Copyright policy )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.
Applied Mathematics, Hausdorff dimension, fractal set, Sobolev function; Bessel potential; fractal set; Minkowski content; Sierpinski carpet, Bessel potential, Sobolev function, Hausdorff and packing measures, Sierpinski carpet, Sobolev spaces, Minkowski content, Fractal set, Bessel potential space, singular point, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis
Applied Mathematics, Hausdorff dimension, fractal set, Sobolev function; Bessel potential; fractal set; Minkowski content; Sierpinski carpet, Bessel potential, Sobolev function, Hausdorff and packing measures, Sierpinski carpet, Sobolev spaces, Minkowski content, Fractal set, Bessel potential space, singular point, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis
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