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Communications in Partial Differential Equations Volume 27, 2002 - Issue 3-4
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Original Articles

UNIFORM SPECTRAL ASYMPTOTICS FOR SINGULARLY PERTURBED LOCALLY PERIODIC OPERATORS

Grégoire Allaire Centre de Mathématiques Apliquées, Ecole Polytechnique, Palaiseau, 91128, France
&
Andrey Piatnitski Narvik Institute of Technology, HiN, P.O. Box 385, Narvik, 8505, Norway; P. N. Lebedev Physical Institute RAS, Leninski prospect 53, Moscow, 17333, Russia
Pages 705-725 | Received 01 Feb 2001, Published online: 07 Feb 2007

Citations (16)

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Iryna Pankratova & Klas Pettersson. (2015) Spectral asymptotics for an elliptic operator in a locally periodic perforated domain. Applicable Analysis 94:6, pages 1207-1234.
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Articles from other publishers (15)

K. Pettersson. (2022) Localization of eigenfunctions in a thin cylinder with a locally periodic oscillating boundary. Journal of Mathematical Analysis and Applications 511:1, pages 126074.
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Klas Pettersson. (2017) Subcritical perturbation of a locally periodic elliptic operator. Mathematical Methods in the Applied Sciences 40:4, pages 1044-1052.
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Alexandra Chechkina, Iryna Pankratova & Klas Pettersson. (2015) Spectral asymptotics for a singularly perturbed fourth order locally periodic elliptic operator. Asymptotic Analysis 93:1-2, pages 141-160.
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Scott N. Armstrong & Panagiotis E. Souganidis. (2013) Concentration phenomena for neutronic multigroup diffusion in random environments. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 30:3, pages 419-439.
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Hermann Douanla. (2012) Homogenization of Steklov Spectral Problems with Indefinite Density Function in Perforated Domains. Acta Applicandae Mathematicae 123:1, pages 261-284.
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V. Chiadò Piat, I. Pankratova & A. Piatnitski. (2013) Localization Effect for a Spectral Problem in a Perforated Domain with Fourier Boundary Conditions. SIAM Journal on Mathematical Analysis 45:3, pages 1302-1327.
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Valeria Chiado Piat, Sergey S. Nazarov & Andrey Piatnitski. (2012) Steklov problems in perforated domains with a coefficient of indefinite sign. Networks & Heterogeneous Media 7:1, pages 151-178.
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Grégoire Allaire, Yves Capdeboscq & Marjolaine Puel. (2012) Homogenization of a one-dimensional spectral problem for a singularly perturbed elliptic operator with Neumann boundary conditions. Discrete & Continuous Dynamical Systems - B 17:1, pages 1-31.
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Sergey A. Nazarov, Iryna L. Pankratova & Andrey L. Piatnitski. (2010) Homogenization of the Spectral Problem for Periodic Elliptic Operators with Sign-Changing Density Function. Archive for Rational Mechanics and Analysis 200:3, pages 747-788.
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G. Cardone, T. Durante & S. A. Nazarov. (2010) The Localization Effect for Eigenfunctions of the Mixed Boundary Value Problem in a Thin Cylinder with Distorted Ends. SIAM Journal on Mathematical Analysis 42:6, pages 2581-2609.
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Grégoire Allaire, Andro Mikelić & Andrey Piatnitski. (2010) Homogenization Approach to the Dispersion Theory for Reactive Transport through Porous Media. SIAM Journal on Mathematical Analysis 42:1, pages 125-144.
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Grégoire Allaire & Rafael Orive. (2007) Homogenization of periodic non self-adjoint problems with large drift and potential. ESAIM: Control, Optimisation and Calculus of Variations 13:4, pages 735-749.
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Grégoire Allaire & Mariapia Palombaro. (2006) Localization for the Schrödinger Equation in a Locally Periodic Medium. SIAM Journal on Mathematical Analysis 38:1, pages 127-142.
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Gr�goire Allaire, Yves Capdeboscq, Andrey Piatnitski, Vincent Siess & M. Vanninathan. (2004) Homogenization of Periodic Systems with Large Potentials. Archive for Rational Mechanics and Analysis 174:2, pages 179-220.
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Grégoire Allaire, Guillaume Bal & Vincent Siess. (2002) Homogenization and localization in locally periodic transport. ESAIM: Control, Optimisation and Calculus of Variations 8, pages 1-30.
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