Acta Mathematica

On the structure of band edges of $2$-dimensional periodic elliptic operators

Nikolay Filonov and Ilya Kachkovskiy

Full-text: Open access

Abstract

For a wide class of $2$-dimensional periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated.

Note

To the memory of Yuri Safarov, our dear friend and colleague

Note

The first author was supported by RFBR Grant 16–01–00087 and by Simons Foundation. The second author was supported by AMS Simons Travel Grant 2014–2016 and by NSF grant DMS–1758326.

Article information

Source
Acta Math., Volume 221, Number 1 (2018), 59-80.

Dates
Received: 26 March 2016
First available in Project Euclid: 19 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.acta/1560966801

Digital Object Identifier
doi:10.4310/ACTA.2018.v221.n1.a2

Mathematical Reviews number (MathSciNet)
MR3877018

Zentralblatt MATH identifier
1407.35072

Keywords
periodic Schrödinger operator Bloch eigenvalues spectral band edges effective mass

Citation

Filonov, Nikolay; Kachkovskiy, Ilya. On the structure of band edges of $2$-dimensional periodic elliptic operators. Acta Math. 221 (2018), no. 1, 59--80. doi:10.4310/ACTA.2018.v221.n1.a2. https://projecteuclid.org/euclid.acta/1560966801


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