Periodic Elliptic Partial Differential Operators

A unique, comprehensive look at the topics arising in studying periodic media, for researchers in mathematics, physics and material science.

Providing a uniquely comprehensive resource for researchers in mathematics, physics, and material science, this book describes the main mathematical objects, problems, tools, and techniques arising in in the last few decades in the booming area of periodic (natural or manufactured) materials, including crystallin materials and photonic crystals.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.