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 identically.
Keywords: minimizer, surfaces of crystals, unorthodox crystal, variational problem
@article{COCV_2007__13_1_72_0, author = {Zaslavski, Alexander J.}, title = {On a variational problem arising in crystallography}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {72--92}, publisher = {EDP-Sciences}, volume = {13}, number = {1}, year = {2007}, doi = {10.1051/cocv:2007003}, mrnumber = {2282102}, zbl = {1136.49012}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007003/} }
TY - JOUR AU - Zaslavski, Alexander J. TI - On a variational problem arising in crystallography JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 72 EP - 92 VL - 13 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007003/ DO - 10.1051/cocv:2007003 LA - en ID - COCV_2007__13_1_72_0 ER -
%0 Journal Article %A Zaslavski, Alexander J. %T On a variational problem arising in crystallography %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 72-92 %V 13 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007003/ %R 10.1051/cocv:2007003 %G en %F COCV_2007__13_1_72_0
Zaslavski, Alexander J. On a variational problem arising in crystallography. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 1, pp. 72-92. doi : 10.1051/cocv:2007003. http://www.numdam.org/articles/10.1051/cocv:2007003/
[1] Wulff theorem and best constant in Sobolev inequality. J. Math. Pures Appl. 71 (1992) 97-118. | Zbl
and ,[2] The Wulff theorem revisited. Proc. R. Soc. Lond. A 432 (1991) 125-145. | Zbl
,[3] Step faceting at the (001) surface of boron doped silicon. Phys. Rev. Lett. 79 (1997) 4226-4229.
, , , and ,[4] A variational problem modelling behavior of unorthodox silicon crystals. ESAIM: COCV 9 (2003) 145-149. | Numdam | Zbl
, and ,[5] Steps on surfaces: experiment and theory. Surface Science Reports 34 (1999) 175-294.
and ,[6] Theory of thermal grooving. J. Appl. Physics 28 (1957) 333-339.
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