On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data
Probability
2009-11-13 v2
Abstract
Consider an inviscid Burgers equation whose initial data is a Levy a-stable process Z with a > 1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller than 1/a, as soon as a is close to 1. This gives a negative answer to a conjecture of Janicki and Woyczynski. Along the way, we contradict a recent conjecture of Z. Shi about the lower tails of integrated stable processes.
Keywords
Cite
@article{arxiv.math/0702260,
title = {On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data},
author = {Thomas Simon},
journal= {arXiv preprint arXiv:math/0702260},
year = {2009}
}