2 results
Hölder continuity of measures for heavy tail potentials
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 22 January 2025, pp. 1-38
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For a class of potentials
$\psi $ satisfying a condition depending on the roof function of a suspension (semi)flow, we show an EKP inequality, which can be interpreted as a Hölder continuity property in the weak
${^*}$ norm of measures, with respect to the pressure of those measures, where the Hölder exponent depends on the 
$L^q$-space to which 
$\psi $ belongs. This also captures a new type of phase transition for intermittent (semi)flows (and maps).
$L^{p}$ ESTIMATES FOR THE HOMOGENIZATION OF STOKES PROBLEM IN A PERFORATED DOMAIN
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 1 / January 2020
- Published online by Cambridge University Press:
- 10 April 2018, pp. 231-258
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- January 2020
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In this paper, we consider the Stokes equations in a perforated domain. When the number of holes increases while their radius tends to 0, it is proven in Desvillettes et al. [J. Stat. Phys. 131 (2008) 941–967], under suitable dilution assumptions, that the solution is well approximated asymptotically by solving a Stokes–Brinkman equation. We provide here quantitative estimates in
$L^{p}$-norms of this convergence.
