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DC Field | Value | Language |
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dc.contributor.author | Plakhov, Alexander | pt_PT |
dc.date.accessioned | 2022-12-14T10:21:42Z | - |
dc.date.available | 2022-12-14T10:21:42Z | - |
dc.date.issued | 2022-10 | - |
dc.identifier.issn | 0944-2669 | pt_PT |
dc.identifier.uri | http://hdl.handle.net/10773/35429 | - |
dc.description.abstract | Let $u$ minimize the functional $F(u) = \int_\Omega f(\nabla u(x))\, dx$ in the class of convex functions $u : \Omega \to {\mathbb R}$ satisfying $0 \le u \le M$, where $\Omega \subset {\mathbb R}^2$ is a compact convex domain with nonempty interior and $M > 0$, and $f : {\mathbb R}^2 \to {\mathbb R}$ is a $C^2$ function, with $\{ \xi : \, \text{the smallest eigenvalue of} \, f''(\xi) \, \text{is zero} \}$ being a closed nowhere dense set in ${\mathbb R}^2$. Let epi$(u)$ denote the epigraph of $u$. Then any extremal point $(x, u(x))$ of epi$(u)$ is contained in the closure of the set of singular points of epi$(u)$. As a consequence, an optimal function $u$ is uniquely defined by the set of singular points of epi$(u)$. This result is applicable to the classical Newton's problem, where $F(u) = \int_\Omega (1 + |\nabla u(x)|^2)^{-1}\, dx$. | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | Springer Nature | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04106%2F2020/PT | pt_PT |
dc.rights | restrictedAccess | pt_PT |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | pt_PT |
dc.title | A solution to Newton’s least resistance problem is uniquely defined by its singular set | pt_PT |
dc.type | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.issue | 5 | pt_PT |
degois.publication.title | Calculus of Variations and Partial Differential Equations | pt_PT |
degois.publication.volume | 61 | pt_PT |
dc.relation.publisherversion | https://doi.org/10.1007/s00526-022-02300-w | pt_PT |
dc.identifier.doi | 10.1007/s00526-022-02300-w | pt_PT |
dc.identifier.essn | 1432-0835 | pt_PT |
dc.identifier.articlenumber | 189 | pt_PT |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2022 CalcVar.pdf | 882.72 kB | Adobe PDF |
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