Characterizing Sobolev spaces of vector-valued functions
| dc.contributor.author | Caamaño Aldemunde, Iván | |
| dc.contributor.author | Jaramillo Aguado, Jesús Ángel | |
| dc.contributor.author | Prieto Yerro, M. Ángeles | |
| dc.date.accessioned | 2023-06-22T10:42:03Z | |
| dc.date.available | 2023-06-22T10:42:03Z | |
| dc.date.issued | 2022 | |
| dc.description | CRUE-CSIC (Acuerdos Transformativos 2022) | |
| dc.description.abstract | We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset Ω⊂RN and a Banach space V, we characterize the functions in the Sobolev-Reshetnyak space R1,p(Ω, V), where 1 ≤p≤∞, in terms of the existence of partial metric derivatives or partial w∗-derivatives with suitable integrability properties. In the case p=∞ the Sobolev-Reshetnyak space R1,∞(Ω, V)is characterized in terms of a uniform local Lipschitz property. We also consider the special case of the space V=l∞. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/72016 | |
| dc.identifier.doi | 10.1016/j.jmaa.2022.126250 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | https://doi.org/10.1016/j.jmaa.2022.126250 | |
| dc.identifier.relatedurl | https://www.sciencedirect.com/science/article/pii/S0022247X22002645 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/71429 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of Mathematical Analysis and Applications | |
| dc.language.iso | eng | |
| dc.page.initial | 126250 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PGC2018-097286-B-I00 | |
| dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/es/ | |
| dc.subject.cdu | 517.982.2 | |
| dc.subject.cdu | 517.983 | |
| dc.subject.keyword | Sobolev spaces | |
| dc.subject.keyword | Vector-valued functions | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Characterizing Sobolev spaces of vector-valued functions | |
| dc.type | journal article | |
| dc.volume.number | 514 | |
| dcterms.references | [1]L. Ambrosio, Metric space valued functions of bounded variation, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4) 17(3) (1990) 439–478. [2]L. Ambrosio, B. Kirchheim, Rectifiable sets in metric and Banach spaces, Math. Ann. 318(3) (2000) 527–555. [3]W. Arendt, M. Kreuter, Mapping theorems for Sobolev spaces of vector-valued functions, Stud. Math. 240 (2018) 275–299. [4]Y. Benyamini, J. Lindenstrauss, Geometric Nonlinear Functional Analysis, Colloquium Publications, vol.48, Amer. Math. Soc., Providence, RI, 2000. [5]I. Caamaño, J.A. Jaramillo, A. Prieto, A. Ruiz de Alarcón, Sobolev spaces of vector-valued functions, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 115(1) (2021) 19. [6]P. Creutz, N. Evseev, An approach to metric space valued Sobolev maps via weak* derivatives, arXiv :2106 .15449, 2021. [7]J. Diestel, J.J. Uhl Jr., Vector Measures, Math Surveys Monogr., vol.15, Amer. Math. Soc., Providence, RI, 1977. [8]J. Duda, Absolutely continuous functions with values in a metric space, Real Anal. Exch. 23(2) (2007) 569–582. [9]S. Eriksson-Bique, G. Giovannardi, R. Korte, N. Shanmugalingam, G. Speight, Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry, J. Differ. Equ. 306 (2022) 590–632. [10]N. Evseev, Vector-valued Sobolev spaces based on Banach function spaces, Nonlinear Anal. 211 (2021) 112479. [11]S.M. Gonek, H.L. Montgomery, Kronecker’s approximation theorem, Indag. Math. 27 (2016) 506–523. [12]P. Hajłasz, J.T. Tyson, Sobolev Peano cubes, Mich. Math. J. 56 (2008) 687–702. [13]J. Heinonen, P. Koskela, N. Shanmugalingam, J.T. Tyson, Sobolev classes of Banach-valued functions and quasiconformal mappings, J. Anal. Math. 85 (2001) 87–139. [14]J. Heinonen, P. Koskela, N. Shanmugalingam, J.T. Tyson, Sobolev Spaces on Metric Measure Spaces. An Approach Based on Upper Gradients, New Math. Monogr., vol.27, Cambridge University Press, Cambridge, 2005. [15]B. Kirchheim, Rectifiable metric spaces: local structure and regularity of the Hausdorff measure, Proc. Am. Math. Soc. 121(1) (1994) 113–123. [16]M. Kreuter, Sobolev Spaces of Vector-Valued Functions, Master Thesis, Ulm University, 2015. [17]J. Malý, W.P. Ziemer, Fine Regularity of Solutions of Elliptic Partial DifferentialEquations, Math. Surveys Monogr., vol.51, American Mathematical Society, Providence, RI, 1997. [18]Yu G. Reshetnyak, Sobolev classes of functions with values in a metric spaces, Sib. Math. J. 38 (1997) 567–583. [19]W. Sierpiński, Sur la question de la mesurabilité de la base de M. Hamel, Fundam. Math. 1 (1920) 105–111. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 139f413f-736a-4f3f-8809-b5677c81a272 | |
| relation.isAuthorOfPublication | 8b6e753b-df15-44ff-8042-74de90b4e3e9 | |
| relation.isAuthorOfPublication | f2a43f90-b551-412e-a95d-2587bbfaa27d | |
| relation.isAuthorOfPublication.latestForDiscovery | 139f413f-736a-4f3f-8809-b5677c81a272 |
Download
Original bundle
1 - 1 of 1
