Publications

G.Cardone, L.Faella, J.C.Nakasato, C.Perugia, Nonlinear coupled system in thin domains with corrugated boundaries for metabolic processes, Annali di Matematica Pura ed Applicata (2024), https://doi.org/10.1007/s10231-024-01442-2.

G. Cardone, W. Jager, J.L. Woukeng, Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers, Mathematical Models and Methods in Applied Sciences 34 (7) (2024), 1343-1400; doi: https://doi.org/10.1142/S0218202524500246. 2.77

G.Cardone, S.A.Nazarov, J. Taskinen, Localization of eigenfunctions in the Dirichlet beaker, Bulletin of the London Mathematical Society 56 (4) (2024), 1362-1384, DOI: https://doi.org/10.1112/blms.13000. 0.95

G.Cardone, S.A.Nazarov, J. Taskinen, Asymptotic expansions of solutions to the Poisson equation with alternating boundary conditions on an open arc, SIAM J. Math. Analysis 55 (6) (2023), 6940-6964; DOI: https://doi.org/10.1137/22M1504214. 2.15

S.Aiyappan, G.Cardone, C.Perugia, Optimal control problem stated in a locally periodic rough domain: a homogenization study, Applicable Analysis (2023); DOI: https://doi.org/10.1080/00036811.2023.2265967. 0,82

G.Cardone, A.Khrabustowskyi, Spectrum of the Laplacian on a Domain Perturbed by Small Resonators, SIAM J. Math. Analysis 55 (4) (2023), 3677--3712; DOI: https://doi.org/10.1137/22M148207X; arXiv:2203.01971. 2.15

G. Cardone, A. Fouetio, S. Talla Lando, J.L. Woukeng, Global dynamics of stochastic tidal equations, Nonlinear Analysis TMA, 225 (2022), 113137; DOI: https://doi.org/10.1016/j.na.2022.113137. 1.45

S.Aiyappan, G.Cardone, C.Perugia, R.Prakash, Homogenization of a nonlinear monotone problem in a locally periodic domain via unfolding method, Nonlinear Analysis: Real World Applications 66 (2022), 103537. DOI: https://doi.org/10.1016/j.nonrwa.2022.103537. 1.40

Cardone, G., Durante, T., Asymptotic analysis of a planar waveguide perturbed by a non periodic perforation, Nanosystems: Physics, Chemistry, Mathematics, 13 (1) (2022), pp. 5–11. DOI: https://doi.org/10.17586/2220-8054-2022-13-1-5-11.

G.Cardone, C.Perugia, M. Villanueva Pesqueira, Asymptotic Behavior of a Bingham Flow in Thin Domains with Rough Boundary, Integr. Equ. Oper. Theory 93 (2021), 24; https://doi.org/10.1007/s00020-021-02643-7; Pdf online. 0,72

D.BORISOV, G.Cardone, G. CHECKHIN, Yu. KOROLEVA, On  elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary, Calculus of Variations and Partial Differential Equations 60 (2021),  48. https://doi.org/10.1007/s00526-020-01847-w. 2,13

G.Cardone, A. FOUETIO, J.L. WOUKENG, Homogenization of a 2D Tidal Dynamics Equation, Mathematics 8 (12) (2020), 2209; https://doi.org/10.3390/math8122209. 

R. BUNOIU, G.Cardone, R. KENGNE, J.L. WOUKENG, Homogenization of 2D Cahn-Hilliard-Navier-Stokes system, J. of Elliptic and Parabolic Equations (2020). DOI: https://doi.org/10.1007/s41808-020-00074-w, arXiv:2005.10209. 0,59

D.BORISOV, G.Cardone, Spectra of operator pencils with small PT-symmetric periodic perturbation, ESAIM: COCV  26 (2020), 2019070, DOI: https://doi.org/10.1051/cocv/2019070. 1,3

G.Cardone, C.Perugia, C.TIMOFTE, Homogenization results for a coupled system of reaction-diffusion equations, Nonlinear Analysis 188 (2019), 236–264, DOI: https://doi.org/10.1016/j.na.2019.06.004, arXiv:1906.05362. 1,43

G.Cardone, A.KHRABUSTOWSKYI, δ′-interaction as a limit of a thin Neumann waveguide with transversal window, Journal of Mathematical Analysis and Applications, 473 (2) (2019), 1320-1342, DOI: http://doi.org/10.1016/j.jmaa.2019.01.024, arXiv:1808.05402. 0,95

G.Cardone, J.L. WOUKENG, Corrector problem in the deterministic homogenization of non- linear elliptic equations, Applicable Analysis (Issue dedicated to V.V.Zhikov), 98 (1-2) (2019), 118-135; DOI: http://doi.org/10.1080/00036811.2018.1448075. 0,7

G.Cardone, T.DURANTE, S.A.NAZAROV, Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation, Journal de Mathématiques Pures Appliquées, 112 (2018), 1-40; DOI: https://doi.org/10.1016/j.matpur.2018.01.002, arXiv:1512.06891. 2,3

R.BUNOIU, G.Cardone, S.A.NAZAROV, Scalar boundary value problems on junctions of thin rods and plates. II. Self-adjoint extensions and simulation models, ESAIM: Mathematical Modeling and Numerical Analysis (M2AN), 52 (2) (2018), 481-508; DOI: https://doi.org/10.1051/m2an/2017047; arXiv:1710.02708. 1,68

G.Cardone, A.KHRABUSTOVSKYI, Spectrum of a singularly perturbed periodic narrow waveguide. J. Math. Anal. Appl. 454 (2) (2017), 673–694, DOI: http://dx.doi.org/10.1016/j.jmaa.2017.05.012; arXiv: 1608.00440. 0,93

F.BAKHAREV, G.Cardone, S.A.NAZAROV, J. TASKINEN, Effects of Rayleigh waves on the essential spectrum in perturbed doubly periodic elliptic problems, Integral Equations and Operator Theory 88 (3) (2017), 373–386; DOI: http://dx.doi.org/10.1007/s00020-017-2379-5; arXiv:1604.02835. 0,85

G.Cardone, T.DURANTE, S.A.NAZAROV, The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions, Journal of Differential. Equations 263 (2) (2017), 1387-1418; DOI: http://dx.doi.org/10.1016/j.jde.2017.03.013; arXiv:1704.05810. 1,95

R.BUNOIU, G.Cardone, Bingham flow in porous media with obstacles of different size. Mathematical Methods in the Applied Sciences 40 (12) (2017), 4514-4528; DOI: http://dx.doi.org/10.1002/mma.4322; arXiv:1701.02992. 0,62

G.Cardone, A.KHRABUSTOVSKYI, Example of periodic Neumann waveguide with gap in spectrum, in J. Dittrich, H. Kovarik, A. Laptev (Eds.), Functional Analysis and Operator Theory for Quantum Physics. Pavel Exner Anniversary Volume, Europ. Math. Soc. Publ. House, 2017, 177-188; DOI: http://dx.doi.org/10.4171/175; arXiv:1605.07812. 

G. BUTTAZZO, G.Cardone, S.A.NAZAROV, Thin Elastic Plates Supported over Small Areas. II: Variational-asymptotic models, Journal of Convex Analysis 24 (3) (2017), 819-855; arXiv:1601.04912. 0,58

G.Cardone, Waveguides with fast oscillating boundary, Nanosystem-Physics Chemistry Mathematics, 8 (2) (2017), 160-165; DOI:  http://dx.doi.org/10.17586/2220-8054-2017-8-2-160-165.

D.BORISOV, G.Cardone, T.DURANTE, Homogenization and uniform resolvent convergence for elliptic operators in a strip perforated along a curve, Proceedings of the Royal Society of Edinburgh Section A: Mathematics (Proc. R. Soc.Edingurgh Sect. A), 146 (6) (2016) 115-1158; DOI: https://doi.org/10.1017/S0308210516000019; arXiv:1305.1009 1,33

G. BUTTAZZO, G.Cardone, S.A.NAZAROV, Thin Elastic Plates Supported over Small Areas. I: Korn’s Inequalities and Boundary Layers, Journal of Convex Analysis 23 (2) (2016), 347-–386; arXiv:1507.03903. 0,57

G.Cardone, S.A.Nazarov, J. Taskinen, Spectra of open waveguides in periodic media, Journal of Functional Analysis 269 (8) (2015), 2328-2364; DOI: http://dx.doi.org/10.1016/j.jfa.2015.08.001. arXiv:1509.01375 1,56

G.Cardone, A.KHRABUSTOVSKYI, Neumann spectral problem in a domain with very corrugated boundary, Journal of Differential Equations 259, n. 6 (2015), 2333–2367; DOI: http://dx.doi.org/10.1016/j.jde.2015.03.031; arXiv:1409.4584. 1,96

R.BUNOIU, G.Cardone, S.A.NAZAROV, Scalar boundary value problems on junctions of thin rods and plates. I. Asymptotic analysis and error estimates, ESAIM: Mathematical Modeling and Numerical Analysis (M2AN) 48 (2014) 1495–1528; DOI: http://dx.doi.org/10.1051/m2an/2014007; arXiv:1403.6029. 1,32

D.BORISOV, G.Cardone, T.DURANTE, Norm-resolvent convergence for elliptic operators in domain with perforation along curve, Comptes Rendus Mathematique Acad. Sci. Paris, Ser. I, 352, n. 9 (2014), 679-683; DOI: http://dx.doi.org/10.1016/j.crma.2014.07.003. 0,57

D.BORISOV, G.Cardone, L.FAELLA, C.Perugia, Uniform resolvent convergence for strip with fast oscillating boundary, Journal of Differential Equations 255, (2013) 4378-4402; DOI: http://dx.doi.org/10.1016/j.jde.2013.08.005; arXiv:1206.1771, journal. 1,61

R.BUNOIU, G.Cardone, C.Perugia, Unfolding Method for the Homogenization of Bingham Flow, in Modeling and Simulation in Fluid Dynamics in Porous Media, Springer Proceedings in Mathematics & Statistics, Vol. 28, 2013; DOI: http://dx.doi.org/10.1007/978-1-4614-5055-9_7; preprint. 

G.Cardone, S.E.PASTUKHOVA, C.Perugia, Estimates in homogenization of degenerate elliptic equations by spectral method, Asymptotic Analysis 81, n.3-4 (2013) 189–209 DOI: http://dx.doi.org/10.3233/ASY-2012-1121. 0,53

G.Cardone, S.A.NAZAROV, K.RUOTSALAINEN, Bound states of a converging quantum waveguide, ESAIM: Mathematical Modeling and Numerical Analysis (M2AN), 47, n.1, (2013), 305-315; DOI: http://dx.doi.org/10.1051/m2an/2012033. 1,39

D.BORISOV, R.BUNOIU, G.Cardone, Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics, Z. Angew. Math. Phys. (ZAMP), 64, n. 3, (2013), 439-472; DOI http://dx.doi.org/10.1007/s00033-012-0264-2; arXiv:1203.0210. 0,69

G.Cardone, R.FARES, G.P.PANASENKO, Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure, Journal of Mathematical Physics 53, 103702 (2012); DOI: http://dx.doi.org/10.1063/1.4746738; arXiv:1201.2121. 0,65

G.Cardone, S.A.NAZAROV, K.RUOTSALAINEN, Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide, Sbornik Mathematichs  203, n. 2, 3-32 (2012); DOI: http://dx.doi.org/10.1070/SM2012v203n02ABEH004217. 0,65

D.BORISOV, G.Cardone, Planar Waveguide with “Twisted” Boundary Conditions: Small Width, Journal of Mathematical Physics 53, 023503 (2012); DOI: http://dx.doi.org/10.1063/1.3681895; arXiv:1112.1787. 0,65

D.BORISOV, G.Cardone, Planar Waveguide with “Twisted” Boundary Conditions: Discrete Spectrum, Journal of Mathematical Physics 52, n. 12, 123513 (2011); DOI: http://dx.doi.org/10.1063/1.3670875; arXiv:1110.3452. 0,6

G.Cardone, L.CARRARO, R.FARES, G.P.PANASENKO, Asymptotic analysis of the steady Stokes equation with randomly perturbed viscosity in a thin tube structure, Journal of Mathematical Sciences, 176, No. 6, (2011), 797-817; DOI: http://dx.doi.org/10.1007/s10958-011-0437-0. 0,2

D.BORISOV, R.BUNOIU, G.Cardone, Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows, Journal of Mathematical Sciences, 176, No. 6, (2011), 774-785; DOI: http://dx.doi.org/10.1007/s10958-011-0435-2. 0,2

D.BORISOV, G.Cardone, Complete asymptotic expansions for the eigenvalues of the Dirichlet Laplacian in thin three-dimensional rods, ESAIM: Control, Optimisation and Calculus of Variations 17 (2011), 887-908; DOI: http://dx.doi.org/10.1051/cocv/2010028; arXiv:0910.3907, Journal 0,98

R.BUNOIU, G.Cardone, T.SUSLINA, Spectral approach to homogenization of an elliptic operator periodic in some directions, Mathematical Methods in the Applied Sciences (MMAS) 34, n.9, (2011), 1075-1096; arXiv/0910.0446. 0,65

D.BORISOV, R.BUNOIU, G.Cardone, On a waveguide with an infinite number of small windows, Comptes Rendus Mathematique Acad. Sci. Paris, Ser. I 349 (2011) 53–56; DOI: http://dx.doi.org/10.1016/j.crma.2010.11.029. 0,54

G.Cardone, S.A.NAZAROV, A.L.PIATNITSKI, On the rate of convergence for perforated plates with a small interior Dirichlet zone, ZAMP, Z. Angew. Math. Phys. 62, n. 3 (2011), 439-468; DOI: http://dx.doi.org/10.1007/s00033-010-0100-5. 0,5

D.BORISOV, R.BUNOIU, G.Cardone, On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition, Ann. Henri Poincaré 11, n. 8 (2010), 1591-1627, DOI: http://dx.doi.org/10.1007/s00023-010-0065-0; arXiv:1010.2072. 0,88

G.Cardone, T.DURANTE, S.A.NAZAROV, The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends, SIAM J. Math. Anal. 42, n. 6, (2010), 2581–2609; http://dx.doi.org/10.1137/090755680; arXiv:0910.1454. 1,56

G.Cardone, T.DURANTE, S.A.NAZAROV, Water-waves modes trapped in a canal by a body with the rough surface, ZAMM, Z. Angew. Math. Mech. 90, No. 12, (2010), 983 — 1004; DOI: http://dx.doi.org/10.1002/zamm.201000042; arXiv:0910.1065. 0,27

G.Cardone, S.A.NAZAROV, J.SOKOLOWSKI, Asymptotic analysis, polarization matrices and topological derivatives for piezoelectric materials with small voids, SIAM Journal on Control and Optimization 48, 6, (2010), 3925-3961; DOI: http://dx.doi.org/10.1137/08073367X; arXiv:0910.1474. 1,12

G.Cardone, S.A.NAZAROV, C.Perugia, A gap in the continuous spectrum of a cylindrical waveguide with a periodic perturbation of the surface, Mathematische Nachrichten 283, n. 9, (2010), 1222–1244; DOI: http://dx.doi.org/10.1002/mana.200910025; arXiv:0910.5679. 0,61

G.Cardone, G.P.PANASENKO, Y.SIRAKOV, Asymptotic analysis and numerical modeling of mass transport in tubular structures, Mathematical Models and Methods in Applied Sciences (M3AS) 20, n. 4 (2010), 1-25. DOI: http://dx.doi.org/10.1142/S0218202510004283; arXiv:0910.5683. 1,34

G.Cardone, A.CORBO ESPOSITO, S.A.NAZAROV, Homogenization of the mixed boundary-value problem for a formally selfadjoint elliptic system in a periodically punched domain, St. Petersburg Math. J. 21 n. 4 (2010), 601–634; http://dx.doi.org/10.1090/S1061-0022-2010-01108-7. 0,62

D.BORISOV, G.Cardone, Homogenization of the planar waveguide with frequently alternating boundary conditions, Journal of Physics A: Mathematical and Theoretical 42, n. 36 (2009) 365205; DOI: http://dx.doi.org/10.1088/1751-8113/42/36/365205; arXiv:0905.0338. 0,5

G.Cardone, S.A.NAZAROV, J. TASKINEN, A criterion for the existence of the essential spectrum for beak-shaped elastic bodies, Journal de Mathématiques Pures Appliquées 92, n.6, (2009) 628–650; DOI: http://dx.doi.org/10.1016/j.matpur.2009.05.007. 1,67

G.Cardone, V.MINUTOLO, S.A.NAZAROV, Gaps in the essential spectrum of periodic elastic waveguides, ZAMM, Z. Angew. Math. Mech., 89, n. 9, (2009) 729-741. DOI: http://dx.doi.org/10.1002/zamm.200800221. 0,43

G.Cardone, S.A.NAZAROV, J.TASKINEN, “Absorption” Effect for Elastic Waves by the Beak-Shaped Boundary Irregularity, Doklady Physics 54, n.3, (2009) 146–150; http://dx.doi.org/10.1134/S1028335809030100. 0,15

G.Cardone, A.CORBO ESPOSITO, S.A.NAZAROV, Korn’s inequality for periodic solids and convergence rate of homogenization, Applicable Analysis 88, n.6, (2009), 847-876. DOI: http://dx.doi.org/10.1080/00036810903042174. 0,62

G.Cardone, S.A.NAZAROV, J.SOKOLOWSKI, Asymptotics of solutions of the Neumann problem in a domain with closely posed components of the boundary, Asymptotic Analysis 62 (2009) 41-88; DOI: http://dx.doi.org/10.3233/ASY-2008-0915. 0,8

G.Cardone, S.A.NAZAROV, J.SOKOLOWSKI, J.TASKINEN, Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain, Comptes Rendus Mechanique 335 (2007) 763-767; DOI: http://dx.doi.org/10.1016/j.crme.2007.10.001. 

G.Cardone, A.CORBO ESPOSITO, S.E.PASTUKHOVA, Homogenization of a scalar problem for a combined structure with singular or thin reinforcement, Zeitschrift für Analysis und ihre Anwendungen (ZAA) 26 (2007) 277-301; DOI: http://dx.doi.org/10.4171/ZAA/1324. 0,68

G.Cardone, A.CORBO ESPOSITO, L.FAELLA, Hausdorff dimension for level sets of upper and lower limits of generalized averages of binary digits, Mathematical Methods in the Applied Sciences (MMAS) 29, 2006, 1983-2008; DOI: http://dx.doi.org/10.1002/mma.764. 0,55

L.BERLYAND, G.Cardone, Y.GORB, G.P.PANASENKO, Asymptotic analysis of an array of closely spaced absolutely conductive inclusions, Networks and Heterogeneous Media, 1, n. 3, 2006, 353-377; DOI: http://dx.doi.org/10.3934/nhm.2006.1.353. 

G.Cardone, A.CORBO ESPOSITO, G.PADERNI, Homogenization of Dirichlet and Neumann problems with gradient constraints, Advances in Mathematical Sciences and Applications 16 (2), 2006, 447-465, article 0,36

G.Cardone, A.CORBO ESPOSITO, G.P.PANASENKO, Asymptotic partial decomposition for diffusion with sorption in thin structures, Nonlinear Analysis 65, 2006, 79-106. DOI: http://dx.doi.org/10.1016/j.na.2005.06.034. 0,61

G.Cardone, S.E.PASTUKHOVA, V.V.ZHIKOV, Some estimates for nonlinear homogenization, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 29 (2005), 101–110; article. 0,12

G.Cardone, A.CORBO ESPOSITO, L.FAELLA, Some remarks about level sets of Cesaro averages of binary digits, Ricerche di Matematica 54 (1), 2005, 11-29. 0,16

G.Cardone, G.GARGIULO, Homogenization of gradient constrained problems with respect to periodic measures, Contemporary Mathematics and Its Applications, 12, 2004; Journal of Mathematical Sciences 130, n.5, 2005, 4941-4953. DOI: http://dx.doi.org/10.1007/s10958-005-0391-9. 

G.Cardone, A.CORBO ESPOSITO, V.V.ZHIKOV, A one dimensional variational problem with gradient constrained, Applicable Analysis 83, n. 7, 2004. DOI: http://dx.doi.org/10.1080/00036810410001658151.

L.CARBONE, G.Cardone, A.CORBO ESPOSITO, Binary digits expansion of numbers: Hausdorff dimensions of intersections of level sets of averages’ upper and lower limits, Scientiae Mathematicae Japonicae 60 (2004), n. 2, 347–356.

G.Cardone, A.CORBO ESPOSITO, G.A.YOSIFIAN, V.V.ZHIKOV, Homogenization of some problems with gradient constraints, Asymptotic Analysis 38, n. 3-4, 2004, pp. 201-220.

F.ACANFORA, G.Cardone S.MORTOLA, On the Variational Convergence of Non-Coercive Quadratic Integral Functionals and Semicontinuity Problems, NoDEA, Nonlinear Differential Equations and Applications, 10, n. 3, 2003, 347 – 373. DOI: http://dx.doi.org/10.1007/s00030-003-1008-y.

G.Cardone, A.CORBO ESPOSITO, V.V.ZHIKOV, An Integral representation result for the Γ-limit of functionals with non standard growth conditions in the case of elasticity, Applicable Analysis, 81, n. 5, 2002, 1179 – 1195. DOI: http://dx.doi.org/10.1080/0003681021000029873.

G.Cardone, C.D’APICE, U.DE MAIO, Homogenization in perforated domains with mixed conditions, NoDEA, Nonlinear Differential Equations and Applications, 9, 2002, 325-346. DOI: http://dx.doi.org/10.1007/s00030-002-8131-z.

G.Cardone, C.D’APICE, U.DE MAIO, Lavrentieff phenomenon and non standard growth conditions, Journal of Convex Analysis 8, n. 2, 2001, 511-532.

G.Cardone, U.DE MAIO, T.DURANTE, On the relaxation of some types of Dirichlet minimum problems for unbounded functionals, Note di Matematica 19, n. 2, 1999, 231-256, http://dx.doi.org/10.1285/i15900932v19n2p231.

G.Cardone, P.DONATO, A.GAUDIELLO, A compactness result for elliptic equations with subquadratic growth in perforated domains, Nonlinear Analysis, Theory, Methods, and Applications 33, 1998, 335-361. DOI: http://dx.doi.org/10.1016/S0362-546X(97)00486-0.

G.Cardone, A.GAUDIELLO, Homogenization of elliptic equations with quadratic growth in periodically perforated domains: the case of unbounded solutions, Portugaliae Mathematica 54, 1997, 51-72.