S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I. Commun. Pure Appl, Math, vol.12, issue.4, pp.623-727, 1959.

S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Communications on Pure and Applied Mathematics, vol.18, issue.1, pp.35-92, 1964.
DOI : 10.5802/aif.111

M. Agranovich, Elliptic Boundary Problems, Partial Differential Equations IX: Elliptic Boundary Problems. Encyclopaedia of Mathematical Sciences, pp.1-144, 1997.
DOI : 10.1007/978-3-662-06721-5_1

N. Auffray, F. Dell-'isola, V. A. Eremeyev, A. Madeo, and G. Rosi, Hamilton???Piola least action principle for second gradient continua and capillary fluids, Mathematics and Mechanics of Solids, vol.119, issue.4, pp.375-417, 2015.
DOI : 10.1137/0125053
URL : https://hal.archives-ouvertes.fr/hal-00836085

G. C. Barozzi, Un problema al contorno non omogeneo in un dominio angoloso per equazioni fortemente quasi-ellittiche in due variabili (I), Rend. Semin. Mat. Univ. Padova, vol.44, pp.27-63, 1970.

G. C. Barozzi, Un problema al contorno non omogeneo in un dominio angoloso per equazioni fortemente quasi-ellittiche in due variabili (II), Rend. Semin. Mat. Univ. Padova, vol.44, pp.319-337, 1970.

A. Battista, C. Cardillo, D. D. Vescovo, N. L. Rizzi, and E. Turco, FREQUENCY SHIFTS INDUCED BY LARGE DEFORMATIONS IN PLANAR PANTOGRAPHIC CONTINUA, Nanomechanics Science and Technology: An International Journal, vol.6, issue.2, pp.161-178, 2015.
DOI : 10.1615/NanomechanicsSciTechnolIntJ.v6.i2.50

O. V. Besov, V. P. Ii-'in, and S. M. Nikol-'skii, Integral Representations of Functions and Imbedding Theorems, Nauka, 1996.

C. Boutin, F. Dell-'isola, I. Giorgio, and L. Placidi, Linear pantographic sheets: Asymptotic micro-macro models identification, Mathematics and Mechanics of Complex Systems, vol.38, issue.2, pp.127-162, 2017.
DOI : 10.1061/(ASCE)NM.2153-5477.0000030
URL : https://hal.archives-ouvertes.fr/hal-01494280

A. Cavallucci, Sulle propriet?? differenziali delle soluzioni delle equazioni quasi-ellittiche, Annali di Matematica Pura ed Applicata, Series 4, vol.59, issue.101, pp.143-167, 1965.
DOI : 10.1007/978-3-642-46175-0

N. Challamel, A. Kocsis, and C. M. Wang, Higher-order gradient elasticity models applied to geometrically nonlinear discrete systems, Teorijska i primenjena mehanika, vol.42, issue.4, pp.223-248, 2015.
DOI : 10.2298/TAM1504223C
URL : https://doi.org/10.2298/tam1504223c

R. Chambon and J. C. Moullet, Uniqueness studies in boundary value problems involving some second gradient models, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.27-29, pp.2771-2796, 2004.
DOI : 10.1016/j.cma.2003.10.017

P. G. Ciarlet, Three-Dimensional Elasticity, Mathematical Elasticity, vol.I, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01077590

N. M. Cordero, S. Forest, and E. P. Busso, Second strain gradient elasticity of nano-objects, Journal of the Mechanics and Physics of Solids, vol.97, 2016.
DOI : 10.1016/j.jmps.2015.07.012
URL : https://hal.archives-ouvertes.fr/hal-01424985

D. Vescovo, D. Giorgio, and I. , Dynamic problems for metamaterials: Review of existing models and ideas for further research, International Journal of Engineering Science, vol.80, pp.153-172, 2014.
DOI : 10.1016/j.ijengsci.2014.02.022
URL : https://hal.archives-ouvertes.fr/hal-00947477

F. Dell-'isola, U. Andreaus, and L. Placidi, At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola, Math. Mech. Solids, vol.20, issue.8, pp.887-928, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00869677

F. Dell-'isola, A. Della-corte, R. Esposito, and L. Russo, Some cases of unrecognized transmission of scientific knowledge: from antiquity to Gabrio Piola's peridynamics and generalized continuum theories, Generalized Continua as Models for Classical and Advanced Materials, pp.77-128, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01316153

F. Dell-'isola, A. Della-corte, and I. Giorgio, Higher-gradient continua: the legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives, Math. Mech. Solids, vol.22, pp.852-872, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01256929

F. Dell-'isola, I. Giorgio, M. Pawlikowski, and N. Rizzi, Large deformations of planar extensible beams and pantographic lattices: heuristic homogenisation, experimental and numerical examples of equilibrium, Proc. R. Soc. Lond. Ser. A, pp.472-20150, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01228588

F. Dell-'isola, M. Porfiri, and S. Vidoli, Piezo-ElectroMechanical (PEM) structures: passive vibration control using distributed piezoelectric transducers, Comptes Rendus M??canique, vol.331, issue.1, pp.69-76, 2003.
DOI : 10.1016/S1631-0721(03)00022-6
URL : https://hal.archives-ouvertes.fr/hal-00496223

F. Dell-'isola, P. Seppecher, and A. Madeo, How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach " á la d'Alember, Z. Angew. Math. Phys, vol.63, issue.6, pp.1119-1141, 2012.

F. Dyson, Characterizing Irregularity, Science, vol.200, issue.4342, pp.677-678, 1978.
DOI : 10.1126/science.200.4342.677

J. F. Eastham and J. S. Peterson, The finite element method in anisotropic sobolev spaces, Computers & Mathematics with Applications, vol.47, issue.10-11, pp.1775-1786, 2004.
DOI : 10.1016/j.camwa.2004.06.020
URL : https://doi.org/10.1016/j.camwa.2004.06.020

Y. V. Egorov and M. A. Shubin, Foundations of the Classical Theory of Partial Differential Equations, Encyclopaedia of Mathematical Sciences, vol.30, 1998.
DOI : 10.1007/978-3-642-58093-2

V. A. Eremeyev and L. P. Lebedev, Existence of weak solutions in elasticity, Mathematics and Mechanics of Solids, vol.1, issue.2, pp.204-217, 2013.
DOI : 10.1007/b98851
URL : https://hal.archives-ouvertes.fr/hal-00831088

S. R. Eugster and F. Dell-'isola, by E. Hellinger, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.49, issue.18, pp.477-506, 2017.
DOI : 10.1016/j.ijsolstr.2012.05.024
URL : https://hal.archives-ouvertes.fr/hal-01568552

L. C. Evans, Partial Differential Equations, Graduate Series in Mathematics Am. Math. Soc, vol.19, 2010.

G. Fichera, Linear Elliptic Differential Systems and Eigenvalue Problems, Lecture Notes in Mathematics, vol.8, 1965.
DOI : 10.1007/BFb0079959

G. Fichera, Existence theorems in elasticity, Handbuch der Physik, pp.347-389, 1972.
DOI : 10.1007/978-3-662-39776-3_3

P. Germain, La méthode des puissances virtuelles en mécanique des milieux continus Première partie: théorie du second gradient, J. Méc, vol.12, pp.236-274, 1973.

P. Germain, The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure, SIAM Journal on Applied Mathematics, vol.25, issue.3, pp.556-575, 1973.
DOI : 10.1137/0125053

I. Giorgio, L. Galantucci, A. Della-corte, D. Vescovo, and D. , Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: Current and upcoming applications, International Journal of Applied Electromagnetics and Mechanics, vol.47, issue.4, pp.1051-1084, 2015.
DOI : 10.3233/JAE-140148
URL : https://hal.archives-ouvertes.fr/hal-01121358

T. J. Healey and S. Krömer, Injective weak solutions in second-gradient nonlinear elasticity, ESAIM: Control, Optimisation and Calculus of Variations, vol.135, issue.4, pp.863-871, 2009.
DOI : 10.1090/S0002-9939-06-08645-X
URL : http://www.esaim-cocv.org/articles/cocv/pdf/2009/04/cocv0775.pdf

L. Hörmander, The Analysis of Linear Partial Differential Operators, II: Differential Operators with Constant Coefficients, A Series of Comprehensive Studies in Mathematics, vol.257, 1983.

M. Kline, Mathematical Thought from Ancient to Modern Times: vols, 1990.

T. S. Kuhn, The Structure of Scientific Revolutions, 1996.

E. N. Kuznetsov, Underconstrained Structural Systems, Mechanical Engineering, 1991.
DOI : 10.1016/0020-7683(88)90026-1

L. P. Lebedev, Vorovich, I.I.: Functional Analysis in Mechanics, 2003.
DOI : 10.1002/zamm.201000200

L. P. Lebedev, I. I. Vorovich, and G. M. Gladwell, Functional Analysis, Applications in Mechanics and Inverse Problems. Solid Mechanics and Its Applications, 2002.

J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, 1972.
DOI : 10.1007/978-3-642-65161-8

A. Mareno and T. J. Healey, Global Continuation in Second-Gradient Nonlinear Elasticity, SIAM Journal on Mathematical Analysis, vol.38, issue.1, pp.103-115, 2006.
DOI : 10.1137/050626065

T. Matsuzawa, On quasi-elliptic boundary problems, Transactions of the American Mathematical Society, vol.133, issue.1, pp.241-265, 1968.
DOI : 10.1090/S0002-9947-1968-0225001-4

R. D. Mindlin and N. N. Eshel, On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures, vol.4, issue.1, pp.109-124, 1968.
DOI : 10.1016/0020-7683(68)90036-X

S. M. Nikol-'skii, ON IMBEDDING, CONTINUATION AND APPROXIMATION THEOREMS FOR DIFFERENTIABLE FUNCTIONS OF SEVERAL VARIABLES, Russian Mathematical Surveys, vol.16, issue.5, p.55, 1961.
DOI : 10.1070/RM1961v016n05ABEH004113

M. Ohno, Y. Shizuta, and T. Yanagisawa, The trace theorem on anisotropic Sobolev spaces, Tohoku Mathematical Journal, vol.46, issue.3, pp.393-401, 1994.
DOI : 10.2748/tmj/1178225719
URL : http://doi.org/10.2748/tmj/1178225719

V. P. Palamodov, Systems of Linear Differential Equations, Mathematical Analysis. Progress in Mathematics, pp.1-35, 1971.
DOI : 10.1007/978-1-4757-1589-7_1

L. Placidi, U. Andreaus, A. Della-corte, and T. Lekszycki, Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients, Zeitschrift f??r angewandte Mathematik und Physik, vol.49, issue.18, pp.3699-3725, 2015.
DOI : 10.1016/j.ijsolstr.2012.05.024

L. Placidi, U. Andreaus, and I. Giorgio, Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model, Journal of Engineering Mathematics, vol.97, issue.1, pp.1-21, 2017.
DOI : 10.1016/j.ijengsci.2015.10.003

L. Placidi, E. Barchiesi, E. Turco, and N. L. Rizzi, A review on 2D models for the description of pantographic fabrics, Zeitschrift f??r angewandte Mathematik und Physik, vol.38, issue.8, p.121, 2016.
DOI : 10.1016/j.compositesa.2007.04.009

L. Placidi, L. Greco, S. Bucci, E. Turco, and N. L. Rizzi, A second gradient formulation for a 2D fabric sheet with inextensible fibres, Zeitschrift f??r angewandte Mathematik und Physik, vol.38, issue.8, p.114, 2016.
DOI : 10.1016/j.compositesa.2007.04.009

H. Reda, Y. Rahali, J. F. Ganghoffer, and H. Lakiss, Wave propagation in 3D viscoelastic auxetic and textile materials by homogenized continuum micropolar models, Composite Structures, vol.141, pp.328-345, 2016.
DOI : 10.1016/j.compstruct.2016.01.071
URL : https://hal.archives-ouvertes.fr/hal-01416422

L. Rodino and P. Boggiatto, Partial differential equations of multi-quasi-elliptic type, Ann. Univ. Ferrara, vol.45, issue.1, pp.275-291, 1999.

D. Scerrato, I. Giorgio, and N. L. Rizzi, Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations, Zeitschrift f??r angewandte Mathematik und Physik, vol.64, issue.1, pp.1-19, 2016.
DOI : 10.1061/(ASCE)NM.2153-5477.0000030
URL : https://hal.archives-ouvertes.fr/hal-01305927

L. I. Sedov, MATHEMATICAL METHODS FOR CONSTRUCTING NEW MODELS OF CONTINUOUS MEDIA, Russian Mathematical Surveys, vol.20, issue.5, p.123, 1965.
DOI : 10.1070/RM1965v020n05ABEH001191

J. Stillwell, Exceptional Objects, The American Mathematical Monthly, vol.105, issue.9, pp.850-858, 1998.
DOI : 10.2307/2589218

R. A. Toupin, Theories of elasticity with couple-stress, Archive for Rational Mechanics and Analysis, vol.17, issue.2, pp.85-112, 1964.
DOI : 10.1007/BF00253050
URL : https://hal.archives-ouvertes.fr/hal-00853382

H. Triebel, Theory of Function Spaces III, Monographs in Mathematics Birkhäuser, vol.100, 2006.
DOI : 10.1007/978-3-0346-0416-1

D. K. Trinh, R. Janicke, N. Auffray, S. Diebels, and S. Forest, EVALUATION OF GENERALIZED CONTINUUM SUBSTITUTION MODELS FOR HETEROGENEOUS MATERIALS, International Journal for Multiscale Computational Engineering, vol.10, issue.6, pp.527-549, 2012.
DOI : 10.1615/IntJMultCompEng.2012003105
URL : https://hal.archives-ouvertes.fr/hal-00718875

E. Turco, K. Barcz, M. Pawlikowski, and N. L. Rizzi, Non-standard coupled extensional and bending bias tests for planar pantographic lattices. Part I: numerical simulations, Zeitschrift f??r angewandte Mathematik und Physik, vol.94, issue.95, p.122, 2016.
DOI : 10.1016/j.ijsolstr.2016.04.017
URL : https://hal.archives-ouvertes.fr/hal-01456148

E. Turco, K. Barcz, and N. L. Rizzi, Non-standard coupled extensional and bending bias tests for planar pantographic lattices. Part II: comparison with experimental evidence, Zeitschrift f??r angewandte Mathematik und Physik, vol.94, issue.95, pp.1-16, 2016.
DOI : 10.1016/j.ijsolstr.2016.04.017
URL : https://hal.archives-ouvertes.fr/hal-01456148

E. Turco, F. Dell-'isola, N. L. Rizzi, R. Grygoruk, W. H. Müller et al., Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence, Mechanics Research Communications, vol.76, pp.86-90, 2016.
DOI : 10.1016/j.mechrescom.2016.07.007
URL : https://hal.archives-ouvertes.fr/hal-01354961

E. Turco, M. Golaszewski, A. Cazzani, and N. L. Rizzi, Large deformations induced in planar pantographic sheets by loads applied on fibers: Experimental validation of a discrete Lagrangian model, Mechanics Research Communications, vol.76, pp.51-56, 2016.
DOI : 10.1016/j.mechrescom.2016.07.001

E. Turco and N. L. Rizzi, Pantographic structures presenting statistically distributed defects: Numerical investigations of the effects on deformation fields, Mechanics Research Communications, vol.77, pp.65-69, 2016.
DOI : 10.1016/j.mechrescom.2016.09.006

N. J. Turro, Paradigms Lost and Paradigms Found: Examples of Science Extraordinary and Science Pathological???And How To Tell the Difference, Angewandte Chemie International Edition, vol.39, issue.13, pp.2255-2259, 2000.
DOI : 10.1002/1521-3773(20000703)39:13<2255::AID-ANIE2255>3.0.CO;2-L

L. R. Volevich, Solubility of boundary value problems for general elliptic systems, Sb. Math, vol.68, issue.110, pp.373-416, 1965.