Regularity of formation of dust in self-similar fragmentations
نویسنده
چکیده
In self-similar fragmentations with a negative index, fragments split even faster as their mass is smaller, so that the fragmentation runs away and some mass is reduced to dust. Our purpose is to investigate the regularity of this formation of dust. Let M(t) denote the mass of dust at time t.We give some sufficient and some necessary conditions for the measure dM to be absolutely continuous. In case of absolute continuity, we obtain an approximation of the density by functions of small fragments. We also study the Hausdorff dimension of the support of dM and the Hölder-continuity of the dust’s mass M .
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