ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - January 2007 - Volume 13, Issue 01  

Research Article

On a variational problem arising in crystallography

Zaslavski, Alexander J.

Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel; ajzasl@tx.technion.ac.il

Abstract

We study a variational problem which was introduced by Hannon, Marcus and Mizel [ESAIM: COCV 9 (2003) 145–149] to describe step-terraces on surfaces of so-called “unorthodox” crystals. We show that there is no nondegenerate intervals on which the absolute value of a minimizer is $\pi/2$ identically.

(Received October 28 2004)

(Revised June 26 2005)

(Online publication February 14 2007)

Key Words:

  • Minimizer;
  • surfaces of crystals;
  • unorthodox crystal;
  • variational problem.

Mathematics Subject Classification:

  • 49J99;
  • 74E15