Eigenvalue problems in 𝐿^{∞}: optimality conditions, duality, and relations with optimal transport

Leon Bungert; Yury Korolev

doi:10.1090/cams/11

Eigenvalue problems in 𝐿^{∞}: optimality conditions, duality, and relations with optimal transport

Leon Bungert, Yury Korolev

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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Abstract

In this article we characterize the $\mathrm{L}^\infty$ eigenvalue problem associated to the Rayleigh quotient $\left.{\|\nabla u\|_{\mathrm{L}^\infty}}\middle/{\|u\|_\infty}\right.$ {and relate it to a divergence-form PDE, similarly to what is known for $\mathrm{L}^p$ eigenvalue problems and the $p$-Laplacian for $p

Original language	English
Pages (from-to)	345-373
Number of pages	29
Journal	Communications of the American Mathematical Society
Volume	2
Issue number	8
DOIs	https://doi.org/10.1090/cams/11
Publication status	Published - 14 Oct 2022

Bibliographical note

This work was funded by the European Unions Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 777826 (NoMADS). The first author acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - GZ 2047/1, Projekt-ID 390685813. The second author was financially supported by the EPSRC (Fellowship EP/V003615/1), the Cantab Capital Institute for the Mathematics of Information at the University of Cambridge and the National Physical Laboratory.

Keywords

math.AP
math.OC
math.SP
26A16, 35P30, 46N10, 47J10, 49R05

Access to Document

10.1090/cams/11Licence: CC BY

Regularisation theory in the data driven setting
Korolev, Y. (PI)
Engineering and Physical Sciences Research Council
1/09/22 → 31/10/24
Project: Research council

Cite this

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abstract = " In this article we characterize the $\mathrm{L}^\infty$ eigenvalue problem associated to the Rayleigh quotient $\left.{\|\nabla u\|_{\mathrm{L}^\infty}}\middle/{\|u\|_\infty}\right.$ {and relate it to a divergence-form PDE, similarly to what is known for $\mathrm{L}^p$ eigenvalue problems and the $p$-Laplacian for $p",

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Eigenvalue problems in 𝐿^{∞}: optimality conditions, duality, and relations with optimal transport

Abstract

Bibliographical note

Keywords

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Regularisation theory in the data driven setting

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