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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: P6724 YEUNG
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:10.1177/1081286518800164
  • 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:10.1177/1081286518776047
  • 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/S0218202518500628
  • 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/S0219530517500105
  • 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/S0219530518500136
  • 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/S0219530515500049
  • 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/S0219530514500237
  • 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 $\r^n$, 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/S0218202513500814
  • 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/S0219530512500121
  • 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/S0218202508002644
  • 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/S0219530507000973
  • 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/S0219530506000681
  • 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/S0219530505000509
  • 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/S0218202503003045
  • 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/S0219530503000235
  • 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:1007621317038
  • 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:1007409220492
  • 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:1007457103654
  • 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 Cârjă. 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