# Interpolation inequalities in pattern formation

@article{Cinti2011InterpolationII, title={Interpolation inequalities in pattern formation}, author={Eleonora Cinti and Felix Otto}, journal={arXiv: Analysis of PDEs}, year={2011} }

We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which was first used by Choksi, Conti, Kohn, and one of the authors in the study of branching in…

## 10 Citations

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Abstract In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the…

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We refine and generalize several interpolation inequalities bounding the $L^p$ norm of a probability density with respect to the reference measure $\mu$ by its Sobolev norm and the Kantorovich…

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