Homogenization of elliptic operators in a strip perforated along a curve
We study the homogenization of a general second order elliptic operator in an infinite planar straight strip perforated by small holes along a curve subject to classical boundary conditions on the holes under rather weak assumptions on the non-periodic perforation. We prove the norm resolvent conver...
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| Published in | AIP conference proceedings Vol. 2116; no. 1 |
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| Main Author | |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Melville
American Institute of Physics
24.07.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0094-243X 1551-7616 |
| DOI | 10.1063/1.5114157 |
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| Abstract | We study the homogenization of a general second order elliptic operator in an infinite planar straight strip perforated by small holes along a curve subject to classical boundary conditions on the holes under rather weak assumptions on the non-periodic perforation. We prove the norm resolvent convergence of the perturbed operator to a homogenized one in various operator norms, the estimates for the rate of convergence and the convergence of the spectrum. |
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| AbstractList | We study the homogenization of a general second order elliptic operator in an infinite planar straight strip perforated by small holes along a curve subject to classical boundary conditions on the holes under rather weak assumptions on the non-periodic perforation. We prove the norm resolvent convergence of the perturbed operator to a homogenized one in various operator norms, the estimates for the rate of convergence and the convergence of the spectrum. |
| Author | Durante, Tiziana |
| Author_xml | – sequence: 1 givenname: Tiziana surname: Durante fullname: Durante, Tiziana organization: University of Salerno, Department of Information Engineering, Electrical Engineering and Applied Mathematics, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy |
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| Editor | Tsitouras, Charalambos Simos, Theodore |
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| References | Bakharev, Cardone, Nazarov, Taskinen (c1) 2017; 88 Kenig, Lin, Shen (c48) 2012; 203 Borisov, Bunoiu, Cardone (c6) 2010; 11 Bunoiu, Cardone, Nazarov (c17) 2014; 48 Pastukhova (c53) 2006; 73 Cardone, Donato, Gaudiello (c25) 1998; 33 Lobo, Oleinik, Perez, Shaposhnikova (c50) 1997; 52 Marchenko, Khruslov (c51) 1974 Borisov, Cardone (c11) 2011; 17 Buttazzo, Cardone, Nazarov (c20) 2016; 23 Chechkin, Koroleva, Meidell, Persson (c39) 2009; 16 Belyaev (c2) 1990; 45 Cardone, Durante, Nazarov (c28) 2018; 112 Bunoiu, Cardone (c16) 2017; 40 Gomez, Lobo, Perez, Shaposhnikova (c44) 2013; 92 Borisov, Cardone, Durante (c14) 2016; 146 Durante, Mel’nyk (c41) 2010; 144 Olejnik, Shamaev, Yosifyan (c52) 1992; 26 Gomez, Lobo, Perez, Shaposhnikova (c45) 2012; 80 Cardone, Nazarov, Ruotsalainen (c33) 2012; 203 Cardone, D’Apice, De Maio (c24) 2002; 9 Birman (c3) 2004; 15 Durante, Mel’nyk, Vashchuk (c40) 2006; 9 Durante, Mel’nyk (c43) 2012; 18 Borisov, Bunoiu, Cardone (c7) 2011; 349 Borisov, Cardone (c12) 2012; 53 Chechkin (c38) 1994; 79 Bunoiu, Cardone, Nazarov (c18) 2018; 52 Griso (c46) 2004; 40 Borisov, Bunoiu, Cardone (c5) 2011; 176 Borisov, Bunoiu, Cardone (c8) 2013; 64 Cardone, Durante, Nazarov (c27) 2017; 263 Cardone, Nazarov, Taskinen (c35) 2015; 269 Cardone, Panasenko, Sirakov (c36) 2010; 20 Cardone, Corbo Esposito, Panasenko (c23) 2006; 65 Cardone, Corbo Esposito, Nazarov (c22) 2010; 21 Cardone, Khrabustovskyi (c29) 2015; 259 Buttazzo, Cardone, Nazarov (c21) 2017; 24 Cardone, Durante, Nazarov (c26) 2010; 90 Borisov, Cardone (c9) 2009; 42 Durante, Rhandi (c42) 2013; 6 Cardone, Nazarov, Taskinen (c34) 2009; 92 Birman, Suslina (c4) 2006; 17 Cardone, Nazarov, Piatnitski (c32) 2011; 62 Borisov, Cardone (c10) 2011; 52 Borisov, Cardone, Faella, Perugia (c15) 2013; 255 Zhikov (c55) 2005; 72 Cardone, Khrabustovskyi (c30) 2017; 454 Borisov, Cardone, Durante (c13) 2014; 352 Oleinik, Perez, Shaposhnikova (c49) 1997; 25 Cardone, Woukeng (c37) 2018 |
| References_xml | – volume: 112 start-page: 1 year: 2018 ident: c28 article-title: Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation publication-title: J. Mathematiques Pures et Appliquees – volume: 16 start-page: 1 year: 2009 ident: c39 article-title: On the Friedrichs Inequality in a Domain Perforated Aperiodically along the Boundary. Homogenization Procedure. Asymptotics for Parabolic Problems publication-title: Russ. J. Math. Phys. – year: 1974 ident: c51 article-title: Boundary Value Problems in Domains with Fine-Grained Boundary publication-title: Naukova Dumka, Kiev – volume: 17 start-page: 897 year: 2006 ident: c4 article-title: Homogenization with corrector term for periodic elliptic differential operators publication-title: St. Petersburg Math. J. – volume: 454 start-page: 673 year: 2017 ident: c30 article-title: Spectrum of a singularly perturbed periodic narrow waveguide publication-title: J. Math. Anal. Appl. – volume: 52 start-page: 838 year: 1997 ident: c50 article-title: On boundary-value problems in domains perforated along manifolds publication-title: Russ. Math. Surv. – volume: 40 start-page: 269 year: 2004 ident: c46 article-title: Error estimate and unfolding for periodic homogenization publication-title: Asymptot. Anal. – volume: 73 start-page: 102 year: 2006 ident: c53 article-title: Some Estimates from Homogenized Elasticity Problems publication-title: Dokl. Math. – volume: 45 start-page: 140 year: 1990 ident: c2 article-title: Averaging of a mixed boundary value problem for the Poisson equation in a domain perforated along the boundary publication-title: Russ. Math. Surv. – volume: 65 start-page: 79 year: 2006 ident: c23 article-title: Asymptotic partial decomposition for diffusion with sorption in thin structures publication-title: Nonlinear Anal. – volume: 9 start-page: 326 year: 2006 ident: c40 article-title: Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction publication-title: Nonlin. Oscil. – volume: 18 start-page: 583 year: 2012 ident: c43 article-title: Homogenization of quasilinear optimal control problems involving a thick multi-level junction of type 3:2:1 publication-title: ESAIM Control Optim. Calc. Var. – volume: 146 start-page: 115 year: 2016 ident: c14 article-title: Homogenization and uniform resolvent convergence for elliptic operators in a strip perforated along a curve publication-title: Proc. R. Soc. Edinb. Sec. A – volume: 48 start-page: 1495 year: 2014 ident: c17 article-title: Scalar boundary value problems on junctions of thin rods and plates. I. Asymptotic analysis and error estimates publication-title: ESAIM Math. Model. Numer. Anal. – volume: 88 start-page: 373 year: 2017 ident: c1 article-title: Effects of Rayleigh waves to essential spectra in composite periodic plane publication-title: Integral Equations and Operator Theory – volume: 52 start-page: 481 year: 2018 ident: c18 article-title: Scalar boundary value problems on junctions of thin rods and plates. II. Self-adjoint extensions and simulation models publication-title: ESAIM Math. Model. Numer. Anal. – volume: 144 start-page: 205 year: 2010 ident: c41 article-title: Asymptotic analysis of an optimal control problem involving a thick two-level junction with alternate type of controls publication-title: J. Optim. Theory Appl. – volume: 80 start-page: 289 year: 2012 ident: c45 article-title: On homogenization of nonlinear Robin type boundary conditions for cavities along manifolds and associated spectral problems publication-title: Asymptot. Anal. – volume: 15 start-page: 507 year: 2004 ident: c3 article-title: On the averaging procedure for periodic operators in a neighborhood of an edge of an internal gap publication-title: St. Petersburg Math. J. – volume: 24 year: 2017 ident: c21 article-title: Thin Elastic Plates Supported over Small Areas. II: Variational-asymptotic models publication-title: J. Convex Anal. – year: 2018 ident: c37 article-title: Corrector problem in the deterministic homogenization of non-linear elliptic equations publication-title: Appl. Anal. – volume: 52 start-page: 123513 year: 2011 ident: c10 article-title: Planar Waveguide with “Twisted” Boundary Conditions: Discrete Spectrum publication-title: J. Math. Phys. – volume: 92 start-page: 628 year: 2009 ident: c34 article-title: A criterion for the existence of the essential spectrum for beak-shaped elastic bodies publication-title: J. Mathematiques Pures Appliquees – volume: 21 start-page: 601 year: 2010 ident: c22 article-title: Homogenization of the mixed boundary-value problem for a formally selfadjoint elliptic system in a periodically punched domain publication-title: St. Petersburg Math. J. – volume: 42 start-page: 365205 year: 2009 ident: c9 article-title: Homogenization of the planar waveguide with frequently alternating boundary conditions publication-title: J. Phys. A. – volume: 23 start-page: 347 year: 2016 ident: c20 article-title: Thin Elastic Plates Supported over Small Areas. I: Korn?s Inequalities and Boundary Layers publication-title: J. Convex Anal. – volume: 33 start-page: 335 year: 1998 ident: c25 article-title: A compactness result for elliptic equations with subquadratic growth in perforated domains publication-title: Nonlin. Anal. Th. Meth. Appl. – volume: 20 start-page: 397 year: 2010 ident: c36 article-title: Asymptotic analysis and numerical modeling of mass transport in tubular structures publication-title: Mathematical Models and Methods in Applied Sciences – volume: 176 start-page: 774 year: 2011 ident: c5 article-title: Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows publication-title: J. Math. Sci. – volume: 64 start-page: 439 year: 2013 ident: c8 article-title: Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics publication-title: Z. Angew. Math. Phys. – volume: 6 start-page: 649 year: 2013 ident: c42 article-title: On the essential self-adjointness of ornstein-uhlenbeck operators perturbed by inverse-square potentials publication-title: Discr. Cont. Dyn. Systems Ser. S – volume: 92 start-page: 218 year: 2013 ident: c44 article-title: Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds publication-title: Appl. Anal. – volume: 79 start-page: 191 year: 1994 ident: c38 article-title: Averaging of boundary value problems with singular perturbation of the boundary conditions publication-title: Russ. Acad. Sci. Sb. Math. – volume: 53 start-page: 023503 year: 2012 ident: c12 article-title: Planar Waveguide with ”Twisted” Boundary Conditions: Small Width publication-title: J. Math. Phys. – volume: 9 start-page: 325 year: 2002 ident: c24 article-title: Homogenization in perforated domains with mixed conditions publication-title: Nonlin. Diff. Eq. Appl. – volume: 11 start-page: 1591 year: 2010 ident: c6 article-title: On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition publication-title: Ann. Henri Poincaré. – volume: 203 start-page: 1009 year: 2012 ident: c48 article-title: Convergence rates in L2 for elliptic homogenization problems publication-title: Arch. Rat. Mech. Anal. – volume: 203 start-page: 3 year: 2012 ident: c33 article-title: Asymptotics of an eigenvalue in the continuous spectrum of a converging waveguide publication-title: Sbornik Mathematichs – volume: 26 year: 1992 ident: c52 article-title: Mathematical Problems in Elasticity and Homogenization publication-title: Stud. Math. Appl. – volume: 90 start-page: 983 year: 2010 ident: c26 article-title: Water-waves modes trapped in a canal by a body with the rough surface publication-title: Z. Angew. Math. Mech. – volume: 255 start-page: 4378 year: 2013 ident: c15 article-title: Uniform resolvent convergence for a strip with fast oscillating boundary publication-title: J. Diff. Equ. – volume: 259 start-page: 2333 year: 2015 ident: c29 article-title: Neumann spectral problem in a domain with very corrugated boundary publication-title: J. Diffent. Eq. – volume: 263 start-page: 1387 year: 2017 ident: c27 article-title: The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions publication-title: J. Diff. Eq. – volume: 72 start-page: 534 year: 2005 ident: c55 article-title: On operator estimates in homogenization theory publication-title: Dokl. Math. – volume: 269 start-page: 2328 year: 2015 ident: c35 article-title: Spectra of open waveguides in periodic media publication-title: J. Funct. Anal. – volume: 25 start-page: 611 year: 1997 ident: c49 article-title: On homogenizations of solutions of boundary value problems in domains, perforated along manifolds publication-title: Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) – volume: 62 start-page: 439 year: 2011 ident: c32 article-title: On the rate of convergence for perforated plates with a small interior Dirichlet zone publication-title: Z. Angew. Math. Phys. – volume: 349 start-page: 53 year: 2011 ident: c7 article-title: On a waveguide with an infinite number of small windows publication-title: Compt. Rend. Math. – volume: 17 start-page: 887 year: 2011 ident: c11 article-title: Complete asymptotic expansions for the eigenvalues of the Dirichlet Laplacian in thin three-dimensional rods publication-title: ESAIM: Control, Optimisation and Calculus of Variations – volume: 352 start-page: 679 year: 2014 ident: c13 article-title: Norm-resolvent convergence for elliptic operators in domain with perforation along curve publication-title: C. R. Mathematique Acad. Sci. Paris, Ser. I – volume: 40 start-page: 4514 year: 2017 ident: c16 article-title: Bingham flow in porous media with obstacles of different size publication-title: Math. Meth. Appl. Sc. |
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| Snippet | We study the homogenization of a general second order elliptic operator in an infinite planar straight strip perforated by small holes along a curve subject to... |
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| SubjectTerms | Boundary conditions Convergence Homogenization Norms Perforation Strip |
| Title | Homogenization of elliptic operators in a strip perforated along a curve |
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