A class of Hamilton-Jacobi equations on Banach-Finsler manifolds
dc.contributor.author | Jaramillo Aguado, Jesús Ángel | |
dc.contributor.author | Jiménez Sevilla, María Del Mar | |
dc.contributor.author | Rodenas Pedregosa, J.L. | |
dc.contributor.author | Sánchez González, L. | |
dc.date.accessioned | 2023-06-19T13:27:53Z | |
dc.date.available | 2023-06-19T13:27:53Z | |
dc.date.issued | 2015 | |
dc.description.abstract | The concept of subdifferentiability is studied in the context of C-1 Finsler manifolds (modeled on a Banach space with a Lipschitz C-1 bump function). A class of Hamilton-Jacobi equations defined on C-1 Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained. | |
dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
dc.description.faculty | Fac. de Ciencias Matemáticas | |
dc.description.refereed | TRUE | |
dc.description.sponsorship | DGES (Spain) | |
dc.description.sponsorship | MEC | |
dc.description.sponsorship | CONICYT-Chile through FONDECYT | |
dc.description.status | pub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/28338 | |
dc.identifier.doi | 10.1016/j.na.2014.09.031 | |
dc.identifier.issn | 0362-546X | |
dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0362546X14003216 | |
dc.identifier.relatedurl | http://arxiv.org/pdf/1407.2977v2.pdf | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/33777 | |
dc.journal.title | Nonlinear Analysis: Theory, Methods & Applications | |
dc.language.iso | eng | |
dc.page.final | 179 | |
dc.page.initial | 159 | |
dc.publisher | Pergamon-Elsevier | |
dc.relation.projectID | MTM2012-34341 | |
dc.relation.projectID | MTM2012-30942 | |
dc.relation.projectID | BES-2013-066316 | |
dc.relation.projectID | 11130354 | |
dc.rights.accessRights | open access | |
dc.subject.cdu | 517.98 | |
dc.subject.keyword | Finsler manifolds | |
dc.subject.keyword | Variational principles | |
dc.subject.keyword | Nonsmooth analysis | |
dc.subject.keyword | Viscosity solutions | |
dc.subject.keyword | Hamilton-Jacobi equations | |
dc.subject.keyword | Geometry of Banach spaces. | |
dc.subject.ucm | Análisis funcional y teoría de operadores | |
dc.title | A class of Hamilton-Jacobi equations on Banach-Finsler manifolds | |
dc.type | journal article | |
dc.volume.number | 113 | |
dcterms.references | [1] P. Angulo Ardoy and L. Guijarro, Balance split sets and Hamilton-Jacobi equations, Calc. Var. Partial Differential Equations 40 (2011), no. 1-2, 223–252. [2] D. Azagra, J. Ferrera and F. López-Mesas, Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds, J. Funct. Anal. 220 (2005), 304-361. [3] D. Azagra, J. Ferrera and F. López-Mesas, A maximum principle for evolution Hamilton-Jacobi equations on Riemannian manifolds, J. Math. Anal. Appl. 323 (2006),473-480. [4] G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques & Applications 17, Springer-Verlag (1994). [5] J.M. Borwein and Q. J. Zhu, Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity, SIAM J. Control Optimization 34 (1996), No. 5, 1568–1591. [6] L.A. Caffarelli and M.G. Crandall, Distance functions and almost global solutions of Eikonal equations, Commu.in Partial Differential Equations 35 (2010), 391–414. [7] M.G. Crandall and P.L. Lions, Hamilton-Jacobi equations in infinite dimensions I. Uniqueness of viscosity solutions, J. Funct. Anal. 62(3) (1985), 379–396. [8] M.G. Crandall and P.L. Lions Hamilton-Jacobi quations in infinite dimensions II. Existence of viscosity solutions, J. Funct. Anal. 65 (1986), 368–405. [9] K. Deimling, Nonlinear Functional Analysis, Springer-Verlang, New York, (1985). [10] R. Deville, Smooth variational principles and non-smooth analysis in Banach spaces, Nonlinear Analysis, Differential Equations and Control Theory, NATO Science Series 528 (1999), 369-405. [11] R. Deville, A mean value theorem for the non differentiable mappings, Serdica Math. 21 (1995), 59-66. [12] R. Deville and E. El Haddad, The viscosity subdifferential of the sum of two functions in Banach Spaces I: First Order Case, Journal of Convex Analysis 32 (1996), 295-308. [13] R. Deville and N. Ghoussoub, Perturbed Minimization Principles and Applications, Handbook of Banach spaces Vol.1, Chapter 10, Editors W. B. Johnson and J. indenstrauss, Elsevier (2003). [14] R. Deville, G. Godefroy and V. Zizler, A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions, J. Funct. Anal. 111 (1993), 197–212. [15] R. Deville, G. Godefroy and V. Zizler, Smoothness and renormings in Banach spaces with applications to Hamilton-Jacobi equations in infinite dimensions, Pitman Monographs Surveys Pure Appl. Math. 64, (1994). [16] E. M. El Haddad, Viscosity solutions of Hamilton-jacobi equations in smooth Banach spaces, Tokyo J. Math. 21(1) (1998), 35–47. [17] E. M. El Haddad, Solutions de viscosité des équations de Hamilton-Jacobi en dimension infinie. Cas stationnaire Publ. Mat. 39(1) (1995), 173–185. [18] H. Ishii, Perron’s method for Hamilton-Jacobi equations, Duke Mathematical Journal 55 (2) (1987), 369–384. [19] H. Ishii, A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations, Hamilton-Jacobi equations: approximations, numerical analysis and applications, 111–249, Lecture Notes in Math. 2074, (2013). [20] M. Jiménez-Sevilla and L. Sánchez-Gonzalez, On some problems on smooth approximation and smooth extension of Lipschitz functions on Banach-Finsler manifolds, Nonlinear Analysis: Theory, Methods and Applications 74 (2011), 3487-3500. [21] S. Ledyaev and Q.J. Zhu, Nonsmooth analysis on smooth manifolds, Trans. Amer. Math. Soc. 359(8) (2007), 3687–3732. [22] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics 69, Springer-Verlag 1994. [23] R.S. Palais, Lusternik-Schnirelman theory on Banach manifolds, Topology 5 (1966), 115-132. [24] P. J. Rabier, Ehresmann fibrations and Palais-Smale conditions for morphisms of Finsler manifolds, Ann. of Math. 146 (1997), 647-691. [25] A. Siconolfi, Metric character of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 355(5) (2003), 1987–2009 | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 8b6e753b-df15-44ff-8042-74de90b4e3e9 | |
relation.isAuthorOfPublication | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 | |
relation.isAuthorOfPublication.latestForDiscovery | 8b6e753b-df15-44ff-8042-74de90b4e3e9 |
Download
Original bundle
1 - 1 of 1