no. 1
On a variational problem arising in crystallography
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 1, pp. 72-92

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 π/2 identically.

DOI : 10.1051/cocv:2007003
Classification : 49J99, 74E15
Keywords: minimizer, surfaces of crystals, unorthodox crystal, variational problem 
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     title = {On a variational problem arising in crystallography},
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     pages = {72--92},
     year = {2007},
     publisher = {EDP Sciences},
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     doi = {10.1051/cocv:2007003},
     mrnumber = {2282102},
     zbl = {1136.49012},
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     url = {https://www.numdam.org/articles/10.1051/cocv:2007003/}
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Zaslavski, Alexander J. On a variational problem arising in crystallography. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 1, pp. 72-92. doi: 10.1051/cocv:2007003

[1] B. Dacorogna and C.E. Pfister, Wulff theorem and best constant in Sobolev inequality. J. Math. Pures Appl. 71 (1992) 97-118. | Zbl

[2] I. Fonseca, The Wulff theorem revisited. Proc. R. Soc. Lond. A 432 (1991) 125-145. | Zbl

[3] J. Hannon, N.C. Bartelt, B.S. Swartzentruber, J.C. Hamilton and G.L. Kellogg, Step faceting at the (001) surface of boron doped silicon. Phys. Rev. Lett. 79 (1997) 4226-4229.

[4] J. Hannon, M. Marcus and V.J. Mizel, A variational problem modelling behavior of unorthodox silicon crystals. ESAIM: COCV 9 (2003) 145-149. | Zbl | Numdam

[5] H.C. Jeng and E.D. Williams, Steps on surfaces: experiment and theory. Surface Science Reports 34 (1999) 175-294.

[6] W.W. Mullins, Theory of thermal grooving. J. Appl. Physics 28 (1957) 333-339.

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