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In this paper we study the structure of minirnizers of variational problems which were introduced by Hannon, Marcus and Mizel (ESAIM Control Optim. Calc. Var., 2003) to describe step-terraces on surfaces of so-called "unorthodox" crystals. These variational problems are associated with two positive parameters. We will show that if one of these parameters is not smali and the second parameter is large, then the rainimizer is a constant function.
Czasopismo
Rocznik
Tom
Strony
157--166
Opis fizyczny
Bibliogr. 8 poz.
Twórcy
autor
- Department of Mathematics Technion-Israel Institute of Technology 32000, Haifa, Israel, ajzasl@techunix.technion.ac.il
Bibliografia
- [1] R.A. Adams, Sobolev spaces, Academic Press, New York, 1975.
- [2] B. Dacorogna and C.E. Pfister, Wulff theorem and best constant in Sobolev inequality, J. Math. Pures Appl., 71 (1992), 97-118.
- [S] I. Fonseca, The Wulff theorem revisited, Proc. R. Soc. Lond. A 432 (1991), 125-145.
- [4] J. Hannon et al, Step faceting at the (001) surface of boron doped silicon, Phys. Rev. Lett. 79 (1997), 4226-4229.
- [5] J. Hannon, M. Marcus and V.J. Mizel, A variational problem modelling behavior of unorthodox silicon crystals, ESAIM Control Optim. Calc. Var. 9 (2003), 145-149.
- [6] H.C. Jeng and E.D. Williams, Steps on surfaces: experiment and theory, Surface Science Reports, 34 (1999), 175-294.
- [7] M. Kurzke and M.O. Rieger, A relaxed model for step-terraces on crystalline surfaces, J. Convex Anal., 11 (2004), 59-67.
- [8] W.W. Mullins, Theory of thermal grooving, J. Appl. Physics 28 (1957), 333-339.
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Bibliografia
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bwmeta1.element.baztech-article-PWA7-0031-0014