Prof. MARDARE Cristinel PhD - University Pierre et Marie Curie (Paris 6) France

HDR - University Pierre et Marie Curie (Paris 6) France


Professor


Contact Information Office: P6724YEUNG
Phone: 34425280
Email: cmardare@cityu.edu.hk

Research Interests Mathematical Elasticity
Differential Geometry
Functional Analysis



Cristinel Mardare received his PhD degree in 1997 from University Pierre et Marie Curie, Paris, France. Before joining City University of Hong Kong, he was Associate Professor at Sorbonne University, formerly University Pierre et Marie Curie. His research uses methods from Functional Analysis, Partial Differential Equations and Differential Geometry to study problems in Solid Mechanics and General Relativity.


Publication Show All Publications Show Prominent Publications
Journal Ciarlet, P. G. & Mardare, C. (2019). A surface in W2p is a locally Lipschitz-continuous function of its fundamental forms in W1p and Lp, p>2. J. Math. Pures Appl. 124. 300- 318. doi:10.1016/j.matpur.2018.06.013
Ciarlet, P. G. , Mardare, C. & Piersanti, P. (2019). An obstacle problem for elliptic membrane shells. Math. Mech. Solids. 24. 1503- 1529. doi:10.1177/1164
Ciarlet, P. G. & Mardare, C. (2019). Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell. C R Acad Sci Paris, Ser. 1. 357. 99- 110. doi:10.1016/j.crma.2018.10.008
Ciarlet, P. G. , Malin, M. & Mardare, C. (2019). Continuity in Fréchet topologies of a surface as a function of its fundamental forms. J. Math. Pures Appl. doi:https://doi.org/10.1016/j.matpur.2019.12.012
Ciarlet, P. G. , Malin, M. & Mardare, C. (2019). Continuity of a surface in Frechet spaces. C. R. Acad. Sci. Paris, Ser. I. doi:10.1016/j.crma.2019.10.010
Ciarlet, P. G. , Malin, M. & Mardare, C. (2019). Continuity of a surface in Fréchet spaces. C. R. Acad. Sci. Paris, Ser. I. 357. 917- 921. doi:https://doi.org/10.1016/j.crma.2019.10.010
Mardare, C. (2019). Nonlinear shell models of Kirchhoff-Love type: existence theorem and comparison with Koiter's model. Acta Mathematicae Applicatae Sinica. 35. 3- 27. doi:10.1007/s10255-019-0800-3
Ciarlet, P. G. & Mardare, C. (2019). The intrinsic theory of linearly elastic plates. Mathematics and Mechanics of Solids. 24. 1182- 1203. doi:10.1177/1047
Ciarlet, P. G. , Mardare, C. & Piersanti, P. (2018). A confinement problem for a linearly elastic membrane shell of elliptic type. C R Acad Sci Paris, Ser. 1. 356. 1040- 1051. doi:10.1016/j.crma.2018.08.002
Ciarlet, P. G. & Mardare, C. (2018). A nonlinear shell model of Koiter's type. C. R. Acad. Sci. Paris, Ser. I. 356. 227- 234. doi:10.1016/j.crma.2017.12.005
Ciarlet, P. G. & Mardare, C. (2018). An existence theorem for a two-dimensional nonlinear shell model of Koiter's type. Math. Models Meth. Applied Sci. 28. 2833- 2861. doi:10.1142/S0628
Ciarlet, P. G. & Mardare, C. (2018). An intrinsic formulation of the Kirchhoff-Love theory of linearly elastic plates. Analysis and Applications. 16. 565- 584. doi:10.1142/S0105
Ciarlet, P. G. & Mardare, C. (2018). Intrinsic formulation of the displacement-traction problem in linear shell theory. C R Acad Sci Paris, Ser. 1. 356. 1243- 1250. doi:10.1016/j.crma.2018.09.007
Ciarlet, P. G. , Malin, M. & Mardare, C. (2018). New estimates of the distance between two surfaces in terms of the distance between their fundamental forms. Analysis and Applications. 17. 363- 392. doi:10.1142/S0136
Malin, M. & Mardare, C. (2018). Nonlinear Korn inequalities on a hypersurface. Chin. Ann. Math., Ser B. 39. 513- 534. doi:10.1007/s11401-018-0080-x
Ciarlet, P. G. , Malin, M. & Mardare, C. (2018). On a vector version of a fundamental lemma of J.L. Lions. Chin. Ann. Math., Ser. B. 39. 33- 46. doi:10.1007/s11401-018-1049-5
Ciarlet, P. G. & Mardare, C. (2018). W2p-estimates for surfaces in terms of their two fundamental forms. C. R. Acad. Sci. Paris, Ser. I. 356. 85- 91. doi:10.1016/j.crma.2017.12.003
Ciarlet, P. G. , Malin, M. & Mardare, C. (2017). New nonlinear estimates for surfaces in terms of their fundamental forms. C. R. Acad. Sci. Paris, Ser. I. 355. 226- 231. doi:10.1016/j.crma.2017.01.002
Malin, M. & Mardare, C. (2017). Nonlinear estimates for hypersurfaces in terms of their fundamental forms. C. R. Acad. Sci. Paris, Ser. I 355. 365. 1196- 1200. doi:10.1016/j.crma.2017.10.014
Ciarlet, P. G. & Mardare, C. (2016). A mathematical model of Koiter's type for a nonlinearly elastic "almost spherical'' shell. C. R. Acad. Sci. Paris, Ser. I. 354. 1241- 1247. doi:10.1016/j.crma.2016.10.011
Ciarlet, P. G. , Hou, Y. & Mardare, C. (2016). On Korn's inequalities on a surface,. Analysis and Applications. 14. 415- 447. doi:10.1142/S0049
Ciarlet, P. G. , Mardare, C. & Mardare, S. (2016). Recovery of immersions from their metric tensors and nonlinear Korn inequalities: A brief survey. Chin. Ann. Math. 37B. 1- 28. doi:10.1007/s11401-016-1070-5
Ciarlet, P. G. , Mardare, C. & Shen, X. (2015). Donati compatibility conditions for membrane and flexural shells. Analysis and Applications. 13. 685- 705. doi:10.1142/S0237
Bunoiu, R. , Ciarlet, P. G. & Mardare, C. (2015). Existence theorem for a nonlinear elliptic shell model. J. Elliptic Parabolic Equations. 1. 31- 48.
Ciarlet, P. G. , Hou, Y. & Mardare, C. (2015). New identity and Korn's inequalities on a surface. C. R. Acad. Sci. Paris, Ser. I. 353. 369- 374. doi:10.1016/j.crma.2014.12.003
Ciarlet, P. G. & Mardare, C. (2015). Nonlinear Korn inequalities in $^n$, with or without boundary conditions. C. R. Acad. Sci. Paris, Ser. I. 353. 563- 568. doi:10.1016/j.crma.2015.03.004
Ciarlet, P. G. & Mardare, C. (2015). Nonlinear Korn inequalities. J. Math. Pures Appl. 104. 1119- 1134. doi:10.1016/j.matpur.2015.07.007
Amrouche, C. , Ciarlet, P. G. & Mardare, C. (2015). On a lemma of Jacques-Louis Lions and its relation to other fundamental results. J. Math. Pures Appl. 104. 207- 226. doi:10.1016/j.matpur.2014.11.007
Ciarlet, P. G. & Mardare, C. (2014). Boundary conditions in intrinsic nonlinear elasticity. J. Math. Pures Appl. 101. 458- 472. doi:10.1016/j.matpur.2013.06.009
Ciarlet, P. G. & Mardare, C. (2014). Intrinsic formulation of the displacement-traction problem in linearized elasticity. Math. Models Meth. Applied Sci. 24. 1197- 1216. doi:10.1142/S0814
Amrouche, C. , Ciarlet, P. G. & Mardare, C. (2014). Remarks on a lemma by Jacques-Louis Lions. C. R. Acad. Sci. Paris, Ser. I. 352. 691- 695. doi:10.1007/978-3-319-18573-6\_11
Grubic, N. , LeFloch, P. & Mardare, C. (2014). The equations of elastostatics in a Riemannian manifold. J. Math. Pures Appl. 102. 1121- 1163. doi:10.1016/j.matpur.2014.07.009
Ciarlet, P. G. & Mardare, C. (2013). Expression of Dirichlet boundary conditions in terms of the Cauchy-Green tensor field. C. R. Math. Acad. Sci. Paris, Ser. I. 351. 323- 327. doi:10.1016/j.crma.2013.05.001
Ciarlet, P. G. & Mardare, C. (2013). Expression of Dirichlet boundary conditions in terms of the strain tensor in linearized elasticity. C. R. Math. Acad. Sci. Paris, Ser. I. 351. 329- 334. doi:10.1016/j.crma.2013.04.015
Ciarlet, P. G. , Gogu, R. & Mardare, C. (2013). Orientation-preserving condition and polyconvexity on a surface - Application to nonlinear shell theory. J. Math. Pures Appl. 99. 704- 725. doi:10.1016/j.matpur.2012.10.006
Ciarlet, P. G. & Mardare, C. (2012). On the Newton-Kantorovich theorem. Analysis and Applications. 10. 249- 269. doi:10.1142/S0121
Mardare, C. (2011). A nonlinear Korn inequality with boundary conditions and its relation to the existence of minimizers in nonlinear elasticity. C. R. Math. Acad. Sci. Paris. 349. 229- 232. doi:10.1016/j.crma.2011.01.011
Ciarlet, P. G. , Gogu, R. & Mardare, C. (2011). A notion of polyconvex function on a surface suggested by nonlinear shell theory. C. R. Math. Acad. Sci. Paris. 349. 1207- 1211. doi:10.1016/j.crma.2011.10.002
Ciarlet, O. G. , Gratie, L. & Mardare, C. (2010). A Cesaro-Volterra formula with little regularity. J. Math. Pures Appl. 93. 41- 60. doi:10.1016/j.matpur.2009.05.011
Ciarlet, P. G. & Mardare, C. (2010). Existence theorems in intrinsic nonlinear elasticity. J. Math. Pures Appl. 94. 229- 243. doi:10.1016/j.matpur.2010.02.002
Ciarlet, P. G. , Gratie, L. & Mardare, C. (2009). A generalization of the classical Ces\`aro-Volterra path integral formula. C. R. Math. Acad. Sci. Paris. 347. 577- 582. doi:10.1016/j.crma.2009.03.007
Ciarlet, P. G. , Gratie, L. & Mardare, C. (2009). Intrinsic methods in elasticity: a mathematical survey. Discrete and Continuous Dynamical Systems (DCDS-A). 23. 133- 164. doi:10.3934/dcds.2009.23.133
LeFloch, P. , Mardare, C. & Mardare, S. (2009). Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity. Discrete and Continuous Dynamical Systems (DCDS-A). 23. 341- 365. doi:10.3934/dcds.2009.23.341
Ciarlet, P. G. & Mardare, C. (2009). The pure displacement problem in nonlinear three-dimensional elasticity: intrinsic formulation and existence theorems. C. R. Math. Acad. Sci. Paris. 347. 677- 683. doi:10.1016/j.crma.2009.03.020
Ciarlet, P. G. , Gratie, L. & Mardare, C. (2008). A new approach to the fundamental theorem of surface theory. Arch. Ration. Mech. Anal. 188. 457- 473. doi:10.1007/s00205-007-0094-0
Mardare, C. (2008). On the derivation of nonlinear shell models from three-dimensional elasticity. Rev. Roumaine Math. Pures Appl. 53. 499- 522.
Ciarlet, P. G. , Gratie, L. , Mardare, C. & Shen, M. (2008). Saint Venant compatibility equations on a surface -- Application to linear intrinsic shell theory. Math. Models Meth. Applied Sci. 18. 165- 194. doi:10.1142/S2644
Ciarlet, P. G. , Gratie, L. , Iosifescu, O. , Mardare, C. & Vallee, C. (2007). Another approach to the fundamental theorem of Riemannian geometry, by way of rotation fields. J. Math. Pures Appl. 87. 237- 252. doi:10.1016/j.matpur.2006.10.009
LeFloch, P. & Mardare, C. (2007). Definition and stability of Lorentzian manifolds with distributional curvature. Port. Math. (N.S.). 64. 535- 573. doi:www.ems-ph.org/doi/10.4171/PM/1794
Ciarlet, P. G. , Gratie, L. & Mardare, C. (2007). New compatibility conditions for the fundamental theorem of surface theory. C. R. Math. Acad. Sci. Paris. 345. 273- 278. doi:10.1016/j.crma.2007.07.014
Ciarlet, P. G. , Mardare, C. & Shen, M. (2007). Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates. C. R. Math. Acad. Sci. Paris. 344. 535- 540. doi:10.1016/j.crma.2007.03.012
Ciarlet, P. G. , Gratie, L. , Mardare, C. & Shen, M. (2007). Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors. C. R. Math. Acad. Sci. Paris. 344. 597- 602. doi:10.1016/j.crma.2007.03.019
Ciarlet, P. G. , Mardare, C. & Shen, M. (2007). Saint Venant compatibility equations in curvilinear coordinates. Analysis and Applications. 5. 231- 251. doi:10.1142/S0973
Ciarlet, P. G. , Gratie, L. & Mardare, C. (2006). A nonlinear Korn inequality on a surface. J. Math. Pures Appl. 85. 2- 16. doi:10.1016/j.matpur.2005.10.010
Mardare, C. (2006). C-infinity regularity of a manifold as a function of its metric tensor. Analysis and Applications. 4. 19- 30. doi:10.1142/S0681
Ciarlet, P. G. , Gratie, L. , Iosifescu, O. , Mardare, C. & Vallee, C. (2006). Rotation fields and the fundamental theorem of Riemannian geometry in R3. C. R. Math. Acad. Sci. Paris. 343. 415- 421. doi:10.1016/j.crma.2006.08.007
Ciarlet, P. G. , Gratie, L. & Mardare, C. (2005). Continuity in H1-norms of surfaces in terms of the L1-norms of their fundamental forms. C.R. Acad. Sci. Paris, Ser. I. 341. 201- 206. doi:10.1016/j.crma.2005.06.031
Ciarlet, P. G. & Mardare, C. (2005). Recovery of a surface with boundary and its continuity as a function of its two fundamental forms. Analysis and Applications. 2. 99- 117. doi:10.1142/S0509
Ciarlet, P. G. & Mardare, C. (2004). An estimate of the H1-norm of deformations in terms of the L1-norm of their Cauchy-Green tensors. C. R. Math. Acad. Sci. Paris, Ser. I. 338. 505- 510. doi:10.1016/j.crma.2004.01.014
Chapelle, D. , Mardare, C. & Munch, A. (2004). Asymptotic considerations shedding light on incompressible shell models. J. of Elasticity. 76. 199- 246. doi:10.1007/s10659-005-0929-6
Ciarlet, P. G. & Mardare, C. (2004). Continuity of a deformation in H1 as a function of its Cauchy-Green tensor in L1. J. of Nonlinear Science. 14. 415- 427. doi:10.1007/s00332-004-0624-y
Ciarlet, P. G. & Mardare, C. (2004). Extension of a Riemannian metric with vanishing curvature. C. R. Math. Acad. Sci. Paris. 338. 391- 396. doi:10.1016/j.crma.2003.12.017
Ciarlet, P. G. & Mardare, C. (2004). On rigid and infinitesimal rigid displacements in shell theory. J. Math. Pures Appl. 83. 1- 15. doi:10.1016/j.matpur.2003.09.004
Ciarlet, P. G. & Mardare, C. (2004). On the recovery of a manifold with boundary in Rn. C. R. Math. Acad. Sci. Paris. 338. 333- 340. doi:10.1016/j.crma.2003.12.018
Ciarlet, P. G. & Mardare, C. (2004). Recovery of a manifold with boundary and its continuity as a function of its metric tensor. J. Math. Pures Appl. 83. 811- 843. doi:10.1016/j.matpur.2004.01.004
Ciarlet, P. G. & Mardare, C. (2003). On rigid and infinitesimal rigid displacements in three-dimensional elasticity. Mathematical Models and Methods in Applied Sciences. 13. 1589- 1598. doi:10.1142/S3045
Ciarlet, P. G. & Mardare, C. (2003). On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory. C. R. Math. Acad. Sci. Paris 336 (2003), 959-966. 336. 959- 966. doi:10.1016/S1631-073X(03)00205-X
Ciarlet, P. G. & Mardare, C. (2003). On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity. C. R. Math. Acad. Sci. Paris. 336. 873- 878. doi:10.1016/S1631-073X(03)00191-2
Mardare, C. (2003). On the recovery of a manifold with prescribed metric tensor. Analysis and Applications. 1. 433- 453. doi:10.1142/S0235
Lods, V. & Mardare, C. (2002). A justification of linear Koiter and Naghdi's models for totally clamped shells. Asymptot. Anal. 31. 189- 210.
Lods, V. & Mardare, C. (2001). A justification of the linear Koiter and Naghdi models for totally clamped shells subjected to non-admissible loads. C. R. Acad. Sci. Paris, Ser I. 333. 151- 154. doi:10.1016/S0764-4442(01)02007-9
Lods, V. & Mardare, C. (2001). Error estimates between the linearized three-dimensional shell equations and Naghdi's model. Asymptot. Anal. 28. 1- 30.
Lods, V. & Mardare, C. (2000). Asymptotic justification of the Kirchhoff-Love assumptions for a linearly elastic clamped shell. J. Elasticity. 58. 105- 154. doi:10.1023/A:1
Lods, V. & Mardare, C. (2000). Error estimates between the three-dimensionnal linearized shell equations and Naghdi's model. C. R. Acad. Sci. Paris 330 (2000), s{\'e}rie I, 157-162. 330. 157- 162. doi:10.1016/S0764-4442(00)00133-6
Lods, V. & Mardare, C. (1999). A justification of Naghdi's shell model. C. R. Acad. Sci. Paris., Ser. I. 328. 951- 954. doi:10.1016/S0764-4442(99)80303-6
Mardare, C. (1998). Asymptotic analysis of linearly elastic shells: error estimates in the membrane case. Asymptotic Analysis. 17. 31- 51.
Lods, V. & Mardare, C. (1998). Asymptotic justification of the Kirchhoff-Love hypotheses for a linearly elastic clamped shell. C. R. Acad. Sci. Paris., Ser. I. 326. 909- 912. doi:10.1016/S0764-4442(98)80059-1
Mardare, C. (1998). The generalized membrane problem for linearly elastic shells with hyperbolic or parabolic middle surface. Journal of Elasticity. 51. 145- 165. doi:10.1023/A:1
Lods, V. & Mardare, C. (1998). The space of inextensional displacements for a partially clamped linearly elastic shell with an elliptic middle surface. Journal of Elasticity. 51. 127- 144. doi:10.1023/A:1
Mardare, C. (1998). Two-dimensional models of linearly elastic shells: error estimates between their solutions. Mathematics and Mechanics of Solids. 3. 303- 318.
Lods, V. & Mardare, C. (1997). Determination of the space of inextensional displacements of a partially clamped linearly elastic shell with a uniformly elliptic middle surface. C. R. Acad. Sci. Paris, Ser. I. 324. 1315- 1320. doi:10.1016/S0764-4442(99)80419-4
Mardare, C. (1996). Error estimates in the asymptotic analysis of linearly elastic shells. C. R. Acad. Sci. Paris, Ser. I. 322. 895- 898.
Mardare, C. (1996). Two-dimensional models of linearly elastic shells: estimates of the difference between their solutions. C. R. Acad. Sci. Paris. 322. 793- 796.


Conference Paper Mardare, C. (2011). Existence of minimizers for the pure displacement problem in nonlinear elasticity. Alexandru Myller Mathematical Seminar - Centennial Conference. AIP Conf. Proc. 1329. (pp. 181- 190). Iasi. Romania:Viorel Barbu and Ovidiu Carj?. doi:10.1063/1.3546084


Book Chapter Mardare, C. (2015). Static elasticity in a riemannian manifold. Differential Geometry and Continuum Mechanics. (pp. 307- 342). Springer. 978-3-319-18572-9. doi:https://doi.org/10.1007/978-3-319-18573-6_11
Ciarlet, P. G. & Mardare, C. (2008). An Introduction to Shell Theory. Differential Geometry: Theory and Applications. (pp. 94- 184). New Jersey. Higher Education Press & World Scientific. 978-981-277-146-9. doi:10.1142/9789812771476_0002




Service in CityU
Teaching Service 2019 - 2020, Calculus and Basic Linear Algebra I.
2019 - 2020, Calculus and Basic Linear Algebra II.
2019 - 2020, Mathematical Methods for Engineering.


Conferences Attended 11 Dec 2019 - 14 Dec 2019, SIAM Conference on Analysis of Partial Differential Equations, USA.
21 Nov 2019 - 22 Nov 2019, HKIAS International Conference on Mathematical Analysis and its Applications, Hong Kong.




Last update date : 09 Dec 2019