## Acta Mathematica

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

#### 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

#### 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