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http://hdl.handle.net/2445/194135
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DC Field | Value | Language |
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dc.contributor.author | Figalli, Alessio | - |
dc.contributor.author | Ros, Xavier | - |
dc.contributor.author | Serra Montolí, Joaquim | - |
dc.date.accessioned | 2023-02-24T16:41:35Z | - |
dc.date.available | 2023-02-24T16:41:35Z | - |
dc.date.issued | 2020-07-02 | - |
dc.identifier.issn | 0073-8301 | - |
dc.identifier.uri | http://hdl.handle.net/2445/194135 | - |
dc.description.abstract | The goal of this paper is to establish generic regularity of free boundaries for the obstacle problem in $\mathbb{R}^n$. By classical results of Caffarelli, the free boundary is $C^{\infty}$ 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 $\mathcal{H}^{n-4}$ measure (in particular, it has codimension 3 inside the free boundary). In particular, for $n \leq 4$, the free boundary is generically a $C^{\infty}$ manifold. This solves a conjecture of Schaeffer (dating back to 1974 ) on the generic regularity of free boundaries in dimensions $n \leq 4$ | - |
dc.format.extent | 112 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1007/s10240-020-00119-9 | - |
dc.relation.ispartof | Publications mathématiques de l'IHÉS, 2020, vol. 132, num. 1, p. 181-292 | - |
dc.relation.uri | https://doi.org/10.1007/s10240-020-00119-9 | - |
dc.rights | (c) Institut des Hautes Études Scientifiques, 2020 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Problemes de contorn | - |
dc.subject.classification | Equacions en derivades parcials | - |
dc.subject.classification | Funcions de variables complexes | - |
dc.subject.classification | Distribució (Teoria de la probabilitat) | - |
dc.subject.other | Boundary value problems | - |
dc.subject.other | Partial differential equations | - |
dc.subject.other | Functions of complex variables | - |
dc.subject.other | Distribution (Probability theory) | - |
dc.title | Generic regularity of free boundaries for the obstacle problem | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 707837 | - |
dc.date.updated | 2023-02-24T16:41:35Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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707837.pdf | 941.22 kB | Adobe PDF | View/Open |
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