Periodic elliptic partial differential operators : the main structures / Peter Kuchment

Format:

Book

Author/Creator:

Kuchment, Peter, 1949- author.

Series:

Cambridge studies in advanced mathematics ; 223.

Cambridge studies in advanced mathematics ; 223

Language:

English

Subjects (All):

Elliptic operators.

Partial differential operators.

Physical Description:

1 online resource

Place of Publication:

Cambridge : Cambridge University Press, 2026

Summary:

"The study of periodic partial differential equations has experienced significant growth in recent decades, driven by emerging applications in fields such as photonic crystals, metamaterials, fluid dynamics, carbon nanostructures, and topological insulators. This book provides a uniquely comprehensive overview for mathematicians, physicists, and material scientists engaged in the analysis and construction of periodic media. It describes all the mathematical objects, tools, problems, and techniques involved. Topics covered are central for areas such as spectral theory of PDEs, homogenization, condensed matter physics and optics. Although it is not a textbook, some basic proofs, background material, and references to an extensive bibliography providing pointers to the wider literature are included to allow graduate students to access the content"-- Cambridge Core

Contents:

Periodic ordinary differential operators

Multidimensional periodicity : Lattices, fundamental domains, and Fourier series

Floquet transform and direct integral decomposition

Dispersion relations : Bloch, Fermi, and Floquet varieties

Spectral structure of periodic elliptic operators

Localized perturbations of periodic operators

Wannier functions

Operators on Abelian coverings of compact manifolds

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed August 6, 2026)

Other Format:

Print version: Kuchment, Peter, 1949- Periodic elliptic partial differential operators

ISBN:

9781009282451

100928245X

OCLC:

1609316481

Publisher Number:

CIPO000412310

Access Restriction:

Restricted for use by site license