Publication: Generic regularity of free boundaries for the obstacle problem
Generic regularity of free boundaries for the obstacle problem
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Figalli, A., Ros-Oton, X., & Serra, J. (2020). Generic regularity of free boundaries for the obstacle problem. Publications Mathématiques de l’IHÉS, 132, 181–292. https://doi.org/10.1007/s10240-020-00119-9
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The goal of this paper is to establish generic regularity of free boundaries for the obstacle problem in Rn. By classical results of Caffarelli, the free boundary is C∞ outside a set of singular points. Explicit examples show that the singular set could be in general (n−1)-dimensional—that is, as large as the regular set. Our main result establishes that, generically, the singular set has zero Hn−4 measure (in particular, it has codimension 3 inside the free boundary). Thus, for n ≤ 4, the free boundary is generically a C∞ manifold. T
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- Figalli, Alessio
- Ros-Oton, Xavier
- Serra, Joaquim
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Figalli, A., Ros-Oton, X., & Serra, J. (2020). Generic regularity of free boundaries for the obstacle problem. Publications Mathématiques de l’IHÉS, 132, 181–292. https://doi.org/10.1007/s10240-020-00119-9
