# American Institute of Mathematical Sciences

June  2017, 6(2): 299-318. doi: 10.3934/eect.2017016

## A note on dimension reduction for unbounded integrals with periodic microstructure via the unfolding method for slender domains

 Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, via Giovanni Paolo Ⅱ, 132,84084 Fisciano (SA), Italy

Received  December 2016 Revised  January 2017 Published  April 2017

A 3D-2D dimension reduction for a nonhomogeneous constrained energy is performed in the realm of $Γ$-convergence, and two-scale convergence for slender domains, providing an integral representation for the limit functional. Applications to supremal functionals are also given.

Citation: Elvira Zappale. A note on dimension reduction for unbounded integrals with periodic microstructure via the unfolding method for slender domains. Evolution Equations & Control Theory, 2017, 6 (2) : 299-318. doi: 10.3934/eect.2017016
##### References:

show all references

##### References:
 [1] Jean-François Babadjian, Francesca Prinari, Elvira Zappale. Dimensional reduction for supremal functionals. Discrete & Continuous Dynamical Systems, 2012, 32 (5) : 1503-1535. doi: 10.3934/dcds.2012.32.1503 [2] Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski. Homogenization of variational functionals with nonstandard growth in perforated domains. Networks & Heterogeneous Media, 2010, 5 (2) : 189-215. doi: 10.3934/nhm.2010.5.189 [3] Joel Fotso Tachago, Giuliano Gargiulo, Hubert Nnang, Elvira Zappale. Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting. Evolution Equations & Control Theory, 2021, 10 (2) : 297-320. doi: 10.3934/eect.2020067 [4] Panpan Ren, Shen Wang. Moderate deviation principles for unbounded additive functionals of distribution dependent SDEs. Communications on Pure & Applied Analysis, 2021, 20 (9) : 3129-3142. doi: 10.3934/cpaa.2021099 [5] Guillaume Bal, Olivier Pinaud, Lenya Ryzhik. On the stability of some imaging functionals. Inverse Problems & Imaging, 2016, 10 (3) : 585-616. doi: 10.3934/ipi.2016013 [6] P. Di Gironimo, L. D’Onofrio. On the regularity of minimizers to degenerate functionals. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1311-1318. doi: 10.3934/cpaa.2010.9.1311 [7] Sandro Zagatti. Existence of minimizers for one-dimensional vectorial non-semicontinuous functionals with second order lagrangian. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021181 [8] Victor Berdichevsky. Distribution of minimum values of stochastic functionals. Networks & Heterogeneous Media, 2008, 3 (3) : 437-460. doi: 10.3934/nhm.2008.3.437 [9] Guillaume Bal, Chenxi Guo, Francçois Monard. Linearized internal functionals for anisotropic conductivities. Inverse Problems & Imaging, 2014, 8 (1) : 1-22. doi: 10.3934/ipi.2014.8.1 [10] Andrea Braides, Antonio Tribuzio. Perturbed minimizing movements of families of functionals. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 373-393. doi: 10.3934/dcdss.2020324 [11] Menita Carozza, Gioconda Moscariello, Antonia Passarelli. Higher integrability for minimizers of anisotropic functionals. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 43-55. doi: 10.3934/dcdsb.2009.11.43 [12] Patrick Cummings, C. Eugene Wayne. Modified energy functionals and the NLS approximation. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1295-1321. doi: 10.3934/dcds.2017054 [13] Nassif Ghoussoub. Superposition of selfdual functionals in non-homogeneous boundary value problems and differential systems. Discrete & Continuous Dynamical Systems, 2008, 21 (1) : 187-220. doi: 10.3934/dcds.2008.21.187 [14] Annibale Magni, Matteo Novaga. A note on non lower semicontinuous perimeter functionals on partitions. Networks & Heterogeneous Media, 2016, 11 (3) : 501-508. doi: 10.3934/nhm.2016006 [15] Angelo B. Mingarelli. Nonlinear functionals in oscillation theory of matrix differential systems. Communications on Pure & Applied Analysis, 2004, 3 (1) : 75-84. doi: 10.3934/cpaa.2004.3.75 [16] Naoufel Ben Abdallah, Irene M. Gamba, Giuseppe Toscani. On the minimization problem of sub-linear convex functionals. Kinetic & Related Models, 2011, 4 (4) : 857-871. doi: 10.3934/krm.2011.4.857 [17] Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki. Lyapunov functionals for multistrain models with infinite delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 507-536. doi: 10.3934/dcdsb.2017025 [18] Guangcun Lu. The splitting lemmas for nonsmooth functionals on Hilbert spaces I. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 2939-2990. doi: 10.3934/dcds.2013.33.2939 [19] René Henrion. Gradient estimates for Gaussian distribution functions: application to probabilistically constrained optimization problems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 655-668. doi: 10.3934/naco.2012.2.655 [20] Thaís Jordão, Xingping Sun. General types of spherical mean operators and $K$-functionals of fractional orders. Communications on Pure & Applied Analysis, 2015, 14 (3) : 743-757. doi: 10.3934/cpaa.2015.14.743

2020 Impact Factor: 1.081