Weak geodesics on prox-regular subsets of Riemannian manifolds
| dc.contributor.author | Ferrera Cuesta, Juan | |
| dc.contributor.author | Pouryayevali, Mohamad R. | |
| dc.contributor.author | Radmanesh, Hajar | |
| dc.date.accessioned | 2023-06-22T10:48:44Z | |
| dc.date.available | 2023-06-22T10:48:44Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | We give a definition of weak geodesics on prox-regular subsets of Riemannian manifolds as continuous curves with some weak regularities. Then obtaining a suitable Lipschitz constant of the projection map, we characterize weak geodesics on a prox-regular set with assigned end points as viscosity critical points of the energy functional. | |
| 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 | FALSE | |
| dc.description.sponsorship | Iran National Science Foundation (INSF) | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/73270 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/71711 | |
| dc.language.iso | eng | |
| dc.relation.projectID | 4002602 | |
| dc.rights | Atribución-NoComercial-CompartirIgual 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-sa/3.0/es/ | |
| dc.subject.cdu | 514.764.2 | |
| dc.subject.cdu | 515.165 | |
| dc.subject.keyword | Prox-regular sets | |
| dc.subject.keyword | ϕ-convex sets | |
| dc.subject.keyword | Sobolev spaces | |
| dc.subject.keyword | Metric projection | |
| dc.subject.keyword | Nonsmooth analysis | |
| dc.subject.keyword | Riemannian manifolds | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Weak geodesics on prox-regular subsets of Riemannian manifolds | |
| dc.type | journal article | |
| dcterms.references | [1] Adams, R.A., Fournier J.J.: Sobolev Spaces. Elsevier (2003) [2] Alexander, S.B., Berg, I.D., Bishop, R.L.: The Riemannian obstacle problem. Illinois J. Math. 31, 167-184 (1987) [3] Azagra, D., Ferrera, J.: Proximal calculus on Riemannian manifolds. Mediterr. J. Math. 2, 437-450 (2005) [4] Azagra, D., Ferrera, J., López-Mesas, F.: Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds. J. Funct. Anal. 220, 304-361 (2005) [5] Barani, A., Hosseini, S., Pouryayevali, M.R.: On the metric projection onto ϕ-convex subsets of Hadamard manifolds. Rev. Mat. Complut. 26, 815-826 (2013) [6] Canino, A.: Existence of a closed geodesic on p-convex sets. Ann. Inst. H. Poincaré C Anal. Non Linéaire. 5, 501-518 (1988) [7] Canino, A.: Local properties of geodesics on p-convex sets. Ann. Mat. Pura Appl. 159(1), 17-44 (1991) [8] Canino, A.: On p-convex sets and geodesics. J. Differential Equations. 75, 118-157 (1988) [9] Clarke, F.H., Ledyaev, Yu.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Graduate Texts in Mathematics 178, Springer, New York (1998) [10] Colombo, G., Thibault, L.: Prox-regular sets and applications. Handbook of Nonconvex Analysis and Applications, D.Y. Gao and D. Motreanu Eds., International Press, Boston, 99-182 (2010) [11] Convent, A., Van Schaftingen, J.: Higher order intrinsic weak differentiability and Sobolev spaces between manifolds. Adv. Calc. Var. 12(3), 303-332 (2019) [12] Convent, A., Van Schaftingen, J.: Intrinsic colocal weak derivatives and Sobolev spaces between manifolds. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16, 97-128 (2016) [13] Degiovanni, M., Marzocchi, M.: A critical point theory for nonsmooth functionals. Ann. Mat. Pura Appl.(4) 167, 73-100 (1994) [14] Degiovanni, M., Morbini, L.: Closed geodesics with Lipschitz obstacle. J. Math. Anal. Appl. 233, 767-789 (1999) [15] do Carmo, M.P.: Riemannian Geometry. Birkhäuser, Boston (1992) [16] Ghimenti, M.: Geodesics in conical manifolds. Topol. Methods Nonlinear Anal. 25(2),235-261 (2005) [17] Hardering, H., Intrinsic discretization error bounds for geodesic finite elements. Doctoral dissertation, Freie Universität Berlin (2015) [18] Hosseini, S., Pouryayevali, M.R.: On the metric projection onto prox-regular subsetsof Riemannian manifolds. Proc. Amer. Math. Soc. 141, 233-244 (2013) [19] Klingenberg, W.P.: Riemannian Geometry. Walter de Gruyter (2011) [20] Lancelotti, S., Marzocchi, M.: Lagrangian systems with Lipschitz obstacle on manifolds. Topol. Methods Nonlinear Anal. 27(2), 229-253 (2006) [21] Lee, J.M.: Introduction to Riemannian Manifolds. Graduate Texts in Mathematics 176, Springer, New York (2018) [22] Marino, A., Scolozzi, D.: Geodetiche con ostacolo. Boll. Un. Mat. Ital. B(6) 2, 1-31(1983) [23] Maury, B., Venel, J.: A mathematical framework for a crowd motion model. C. R. Math. Acad. Sci. Paris. 346, 1245–1250 (2008) [24] Poliquin, R.A., Rockafellar, R.T.: Prox-regular functions in variational analysis. Trans. Amer. Math. Soc.348, 1805-1838 (1996) [25] Pouryayevali, M.R., Radmanesh, H.: Minimizing curves in proxregular subsets of Riemannian manifolds. Set-Valued and Var. Anal. (2021). https://doi.org/10.1007/s11228-021-00614-z [26] Pouryayevali, M.R., Radmanesh, H.: Sets with the unique footpoint property and ϕ-convex subsets of Riemannian manifolds. J. Convex Anal. 26, 617-633 (2019) [27] Sakai, T.: Riemannian Geometry. Translations of Mathematical Monographs 149. American Mathematical Society (1996) [28] Schwartz, J.T.: Generalizing the Lusternik-Schnirelman theory of critical points. Comm. Pure Appl. Math. 17, 307-315 (1964) [29] Scolozzi, D.: Un risultato di locale unicità per le geodetiche su varietà con bordo. Boll. Un. Mat. Ital. B (6) 5, 309-327 (1986) [30] Serre, J.P.: Homologie singulière des espaces fibrés. Ann. of Math. 54, 425-505 (1951) [31] Tanwani, A., Brogliato, B., Prieur, C.: Stability and observer design for Lur’e systems with multivalued, nonmonotone, time-varying nonlinearities and state jumps. SIAM J. Control Optim. 52, 3639–3672 (2014) [32] Wehrheim, K.: Uhlenbeck compactness. European Mathematical Society (2004) [33] Wolter, F.E.: Interior metric shortest paths and loops in Riemannian manifolds with not necessarily smooth boundary. preprint (1979) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 1a91d6af-aaeb-4a3e-90ce-4abdf2b90ac3 | |
| relation.isAuthorOfPublication.latestForDiscovery | 1a91d6af-aaeb-4a3e-90ce-4abdf2b90ac3 |
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