Estimates on translations and Taylor expansions in fractional Sobolev spaces
| dc.contributor.author | Del Teso Méndez, Félix | |
| dc.contributor.author | Gómez-Castro, D. | |
| dc.contributor.author | Vázquez, Juan Luis | |
| dc.date.accessioned | 2023-06-17T08:28:50Z | |
| dc.date.available | 2023-06-17T08:28:50Z | |
| dc.date.issued | 2020-11 | |
| dc.description.abstract | In this paper we study how the (normalised) Gagliardo semi-norms [u]Ws,p(Rn) control translations. In particular, we prove that ‖u(⋅+y)−u‖Lp(Rn)≤C[u]Ws,p(Rn)|y|s for n≥1, s∈[0,1] and p∈[1,+∞], where C depends only on n. We then obtain a corresponding higher-order version of this result: we get fractional rates of the error term in the Taylor expansion. We also present relevant implications of our two results. First, we obtain a direct proof of several compact embedding of Ws,p(Rn) where the Fréchet–Kolmogorov Theorem is applied with known rates. We also derive fractional rates of convergence of the convolution of a function with suitable mollifiers. Thirdly, we obtain fractional rates of convergence of finite-difference discretisations for Ws,p(Rn). | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/73991 | |
| dc.identifier.doi | 10.1016/j.na.2020.111995 | |
| dc.identifier.issn | 0362-546X | |
| dc.identifier.officialurl | https://doi.org/10.1016/j.na.2020.111995 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/7245 | |
| dc.journal.title | Nonlinear Analysis: Theory, Methods & Applications | |
| dc.language.iso | eng | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PGC2018-094522-B-I00; PGC2018-098440-B-I00 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Functional analysis | |
| dc.subject.keyword | Sobolev spaces | |
| dc.subject.keyword | Linear function spaces | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Estimates on translations and Taylor expansions in fractional Sobolev spaces | |
| dc.type | journal article | |
| dc.volume.number | 200 | |
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| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5400d9ae-bfa7-4205-850d-f9e34a361fa6 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5400d9ae-bfa7-4205-850d-f9e34a361fa6 |
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