Nakasato, Jean Carlos; Pereira, Marcone Corrêa A classical approach for the \(p\)-Laplacian in oscillating thin domains. (English) Zbl 1483.35017 Topol. Methods Nonlinear Anal. 58, No. 1, 209-231 (2021). MSC: 35B27 35B25 35B40 35J25 35J92 PDFBibTeX XMLCite \textit{J. C. Nakasato} and \textit{M. C. Pereira}, Topol. Methods Nonlinear Anal. 58, No. 1, 209--231 (2021; Zbl 1483.35017) Full Text: DOI
Gaudiello, Antonio; Guibé, Olivier Homogenization of an evolution problem with \( L\log L\) data in a domain with oscillating boundary. (English) Zbl 1391.35036 Ann. Mat. Pura Appl. (4) 197, No. 1, 153-169 (2018). Reviewer: Marcus Waurick (Glasgow) MSC: 35B27 35J25 35R05 PDFBibTeX XMLCite \textit{A. Gaudiello} and \textit{O. Guibé}, Ann. Mat. Pura Appl. (4) 197, No. 1, 153--169 (2018; Zbl 1391.35036) Full Text: DOI
Gaudiello, Antonio; Guibé, Olivier; Murat, François Homogenization of the brush problem with a source term in \(L^{1}\). (English) Zbl 1371.35067 Arch. Ration. Mech. Anal. 225, No. 1, 1-64 (2017). MSC: 35J25 PDFBibTeX XMLCite \textit{A. Gaudiello} et al., Arch. Ration. Mech. Anal. 225, No. 1, 1--64 (2017; Zbl 1371.35067) Full Text: DOI
Barros, Saulo R. M.; Pereira, Marcone C. Semilinear elliptic equations in thin domains with reaction terms concentrating on boundary. (English) Zbl 1338.35176 J. Math. Anal. Appl. 441, No. 1, 375-392 (2016). MSC: 35J61 35B40 PDFBibTeX XMLCite \textit{S. R. M. Barros} and \textit{M. C. Pereira}, J. Math. Anal. Appl. 441, No. 1, 375--392 (2016; Zbl 1338.35176) Full Text: DOI
De Maio, U.; Faella, L.; Perugia, C. Optimal control for a second-order linear evolution problem in a domain with oscillating boundary. (English) Zbl 1325.49005 Complex Var. Elliptic Equ. 60, No. 10, 1392-1410 (2015). MSC: 49J20 35B27 PDFBibTeX XMLCite \textit{U. De Maio} et al., Complex Var. Elliptic Equ. 60, No. 10, 1392--1410 (2015; Zbl 1325.49005) Full Text: DOI
Pereira, Marcone C.; Silva, Ricardo P. Correctors for the Neumann problem in thin domains with locally periodic oscillatory structure. (English) Zbl 1329.35040 Q. Appl. Math. 73, No. 3, 537-552 (2015). MSC: 35B25 35B27 74Kxx 35J25 PDFBibTeX XMLCite \textit{M. C. Pereira} and \textit{R. P. Silva}, Q. Appl. Math. 73, No. 3, 537--552 (2015; Zbl 1329.35040) Full Text: DOI arXiv
Pereira, Marcone C. Parabolic problems in highly oscillating thin domains. (English) Zbl 1321.35081 Ann. Mat. Pura Appl. (4) 194, No. 4, 1203-1244 (2015). Reviewer: Alain Brillard (Riedisheim) MSC: 35K20 35B25 35B27 35B40 35B41 35K91 74Q10 PDFBibTeX XMLCite \textit{M. C. Pereira}, Ann. Mat. Pura Appl. (4) 194, No. 4, 1203--1244 (2015; Zbl 1321.35081) Full Text: DOI arXiv
Mel’nyk, Taras A. Asymptotic approximation for the solution to a semi-linear parabolic problem in a thick junction with the branched structure. (English) Zbl 1515.35037 J. Math. Anal. Appl. 424, No. 2, 1237-1260 (2015). MSC: 35B27 35C20 35K20 35K58 PDFBibTeX XMLCite \textit{T. A. Mel'nyk}, J. Math. Anal. Appl. 424, No. 2, 1237--1260 (2015; Zbl 1515.35037) Full Text: DOI arXiv
Arrieta, José M.; Pereira, Marcone C. The Neumann problem in thin domains with very highly oscillatory boundaries. (English) Zbl 1304.35056 J. Math. Anal. Appl. 404, No. 1, 86-104 (2013). MSC: 35B27 PDFBibTeX XMLCite \textit{J. M. Arrieta} and \textit{M. C. Pereira}, J. Math. Anal. Appl. 404, No. 1, 86--104 (2013; Zbl 1304.35056) Full Text: DOI arXiv
Gaudiello, Antonio; Guibé, Olivier Homogenization of an elliptic second-order problem with \(L\log L\) data in a domain with oscillating boundary. (English) Zbl 1284.35050 Commun. Contemp. Math. 15, No. 6, Article ID 1350008, 13 p. (2013). Reviewer: Alain Brillard (Riedisheim) MSC: 35B27 35J25 35R05 PDFBibTeX XMLCite \textit{A. Gaudiello} and \textit{O. Guibé}, Commun. Contemp. Math. 15, No. 6, Article ID 1350008, 13 p. (2013; Zbl 1284.35050) Full Text: DOI
Chechkina, T. P. Averaging in cascade junctions with a “wide” transmission domain. (English. Russian original) Zbl 1277.74063 J. Math. Sci., New York 190, No. 1, 157-169 (2013); translation from Sovrem. Mat., Fundam. Napravl. 39, 151-162 (2011). MSC: 74Q05 35Q74 35B27 35J25 74K30 PDFBibTeX XMLCite \textit{T. P. Chechkina}, J. Math. Sci., New York 190, No. 1, 157--169 (2013; Zbl 1277.74063); translation from Sovrem. Mat., Fundam. Napravl. 39, 151--162 (2011) Full Text: DOI
Moussa, Abdelaziz Aït; Zlaïji, Loubna Dimension reduction and homogenization of random degenerate operators. I. (English) Zbl 1295.35050 LMS J. Comput. Math. 15, 1-22 (2012). MSC: 35B27 35J60 35R60 60G57 60H25 PDFBibTeX XMLCite \textit{A. A. Moussa} and \textit{L. Zlaïji}, LMS J. Comput. Math. 15, 1--22 (2012; Zbl 1295.35050) Full Text: DOI
Mel’nyk, T. A.; Nakvasiuk, Iu. A. Homogenization of a parabolic Signorini boundary value problem in a thick plane junction. (English. Russian original) Zbl 1348.35022 J. Math. Sci., New York 181, No. 5, 613-631 (2012); translation from Probl. Mat. Anal. 63, 67-82 (2012). MSC: 35B27 35D30 35K20 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{Iu. A. Nakvasiuk}, J. Math. Sci., New York 181, No. 5, 613--631 (2012; Zbl 1348.35022); translation from Probl. Mat. Anal. 63, 67--82 (2012) Full Text: DOI
Mel’nyk, T. A.; Nakvasiuk, Iu. A.; Wendland, W. L. Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem. (English) Zbl 1217.35019 Math. Methods Appl. Sci. 34, No. 7, 758-775 (2011). Reviewer: Alain Brillard (Riedisheim) MSC: 35B27 35J20 47J05 74K30 35J86 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} et al., Math. Methods Appl. Sci. 34, No. 7, 758--775 (2011; Zbl 1217.35019) Full Text: DOI
Mel’nik, T. A.; Sadovyi, D. Yu. Homogenization of elliptic problems with alternating boundary conditions in a thick two-level junction of type 3:2:2. (English. Russian original) Zbl 1311.35016 J. Math. Sci., New York 165, No. 1, 81-104 (2010); translation from Probl. Mat. Anal. 44, 73-92 (2010). MSC: 35B27 35J25 35J05 PDFBibTeX XMLCite \textit{T. A. Mel'nik} and \textit{D. Yu. Sadovyi}, J. Math. Sci., New York 165, No. 1, 81--104 (2010; Zbl 1311.35016); translation from Probl. Mat. Anal. 44, 73--92 (2010) Full Text: DOI
Vinh, Pham Chi; Tung, Do Xuan Homogenized equations of the linear elasticity in two-dimensional domains with very rough interfaces. (English) Zbl 1272.74044 Mech. Res. Commun. 37, No. 3, 285-288 (2010). MSC: 74B05 74Q05 PDFBibTeX XMLCite \textit{P. C. Vinh} and \textit{D. X. Tung}, Mech. Res. Commun. 37, No. 3, 285--288 (2010; Zbl 1272.74044) Full Text: DOI Link
Chechkin, G. A.; D’Apice, C.; De Maio, U. On the rate of convergence of solutions in domain with periodic multilevel oscillating boundary. (English) Zbl 1205.35020 Math. Methods Appl. Sci. 33, No. 17, 2019-2036 (2010). MSC: 35B27 76M50 35P05 35B25 35J25 PDFBibTeX XMLCite \textit{G. A. Chechkin} et al., Math. Methods Appl. Sci. 33, No. 17, 2019--2036 (2010; Zbl 1205.35020) Full Text: DOI
Chechkin, G. A.; Chechkina, T. P.; D’Apice, C.; de Maio, U.; Mel’nyk, T. A. Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction. (English) Zbl 1196.35035 Russ. J. Math. Phys. 17, No. 1, 35-55 (2010). Reviewer: Adrian Muntean (Eindhoven) MSC: 35B27 35J05 35B25 PDFBibTeX XMLCite \textit{G. A. Chechkin} et al., Russ. J. Math. Phys. 17, No. 1, 35--55 (2010; Zbl 1196.35035) Full Text: DOI
Kazmerchuk, Yu. A.; Mel’nyk, T. A. Homogenization of the Signorini boundary-value problem in a thick plane junction. (English) Zbl 1277.35035 Nonlinear Oscil., N.Y. 12, No. 1, 45-59 (2009) and Nelinijni Kolyvannya 12, No. 1, 44-58 (2009). MSC: 35B27 35J86 PDFBibTeX XMLCite \textit{Yu. A. Kazmerchuk} and \textit{T. A. Mel'nyk}, Nonlinear Oscil., N.Y. 12, No. 1, 45--59 (2009; Zbl 1277.35035) Full Text: DOI arXiv
Cho, Ilwoo; Jorgensen, Palle E. T. Applications of automata and graphs: labeling operators in Hilbert space. II. (English) Zbl 1293.46034 J. Math. Phys. 50, No. 6, 063511, 42 p. (2009). MSC: 46L10 05C63 37B15 46C05 47A99 47L99 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, J. Math. Phys. 50, No. 6, 063511, 42 p. (2009; Zbl 1293.46034) Full Text: DOI arXiv
Mel’nik, T. A.; Chechkin, G. A.; Chechkina, T. P. Convergence theorems for solutions and energy functionals of boundary value problems in thick multilevel junctions of a new type with perturbed Neumann conditions on the boundary of thin rectangles. (English. Russian original) Zbl 1207.35045 J. Math. Sci., New York 159, No. 1, 113-132 (2009); translation from Probl. Mat. Anal. 40, 113-132 (2009). Reviewer: Alain Brillard (Riedisheim) MSC: 35B27 35B40 35J25 PDFBibTeX XMLCite \textit{T. A. Mel'nik} et al., J. Math. Sci., New York 159, No. 1, 113--132 (2009; Zbl 1207.35045); translation from Probl. Mat. Anal. 40, 113--132 (2009) Full Text: DOI
Amirat, Youcef; Bodart, Olivier; De Maio, Umberto; Gaudiello, Antonio Asymptotic approximation of the solution of Stokes equations in a domain with highly oscillating boundary. (English) Zbl 1248.76038 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 53, No. 2, 135-148 (2007). MSC: 76D07 35B25 35Q35 PDFBibTeX XMLCite \textit{Y. Amirat} et al., Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 53, No. 2, 135--148 (2007; Zbl 1248.76038) Full Text: DOI
Mossino, J.; Sili, Ali Limit behavior of thin heterogeneous domain with rapidly oscillating boundary. (English) Zbl 1387.35036 Ric. Mat. 56, No. 1, 119-148 (2007). MSC: 35B27 35J60 PDFBibTeX XMLCite \textit{J. Mossino} and \textit{A. Sili}, Ric. Mat. 56, No. 1, 119--148 (2007; Zbl 1387.35036) Full Text: DOI
Blanchard, Dominique; Gaudiello, Antonio; Griso, Georges Junction of a periodic family of elastic rods with a thin plate. II. (English) Zbl 1127.74025 J. Math. Pures Appl. (9) 88, No. 2, 149-190 (2007). MSC: 74K30 74Q05 74K10 74K20 35B27 PDFBibTeX XMLCite \textit{D. Blanchard} et al., J. Math. Pures Appl. (9) 88, No. 2, 149--190 (2007; Zbl 1127.74025) Full Text: DOI