Extended Rearrangement Inequalities and Applications to Some Quantitative Stability Results

@article{Lemou2016ExtendedRI,
  title={Extended Rearrangement Inequalities and Applications to Some Quantitative Stability Results},
  author={Mohammed Lemou},
  journal={Communications in Mathematical Physics},
  year={2016},
  volume={348},
  pages={695-727}
}
In this paper, we prove a new functional inequality of Hardy–Littlewood type for generalized rearrangements of functions. We then show how this inequality provides quantitative stability results of steady states to evolution systems that essentially preserve the rearrangements and some suitable energy functional, under minimal regularity assumptions on the perturbations. In particular, this inequality yields a quantitative stability result of a large class of steady state solutions to the… CONTINUE READING

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