Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 3, pp. 573-591. 
@article{M2AN_1999__33_3_573_0,
     author = {Bonnetier, Eric and Falk, Richard S. and Grinfeld, Michael A.},
     title = {Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {573--591},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {3},
     year = {1999},
     mrnumber = {1713239},
     zbl = {0958.74022},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1999__33_3_573_0/}
}
TY  - JOUR
AU  - Bonnetier, Eric
AU  - Falk, Richard S.
AU  - Grinfeld, Michael A.
TI  - Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 573
EP  - 591
VL  - 33
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/M2AN_1999__33_3_573_0/
LA  - en
ID  - M2AN_1999__33_3_573_0
ER  - 
%0 Journal Article
%A Bonnetier, Eric
%A Falk, Richard S.
%A Grinfeld, Michael A.
%T Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 573-591
%V 33
%N 3
%I EDP-Sciences
%U http://archive.numdam.org/item/M2AN_1999__33_3_573_0/
%G en
%F M2AN_1999__33_3_573_0
Bonnetier, Eric; Falk, Richard S.; Grinfeld, Michael A. Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 3, pp. 573-591. http://archive.numdam.org/item/M2AN_1999__33_3_573_0/

[1] J. M. Ball and V. J. Mizel, One-dimensional variational problems whose minimizers do not satisfy the Euler Lagrange equation.Arch. Rational Mech. Anal 90 (1985) 325-388. | MR | Zbl

[2] C. Bandle, Isoperimetric Inequalities and Applications. Pitman (1980). | MR | Zbl

[3] B. Dacorogna, Direct Methods in the Calculus of Variations. Springer-Verlag, Berlin, New York (1989). | MR | Zbl

[4] Solids Far From Equilibrium. C. Godresche Ed., Cambridge University Press (1991). | MR

[5] J. W. Gibbs, On the equilibrium of heterogeneous substances. Trans. Connect. Acad. Sci. 3 (1876-1878) 108-248, 343-524. | JFM

[6] E. Giusti, Minimal surfaces and functions of bounded variation. Birkhauser, Boston (1984). | MR | Zbl

[7] M. A. Grinfeld, Thermodynamic Methods in the Theory of Heterogeneous Systems. Longman (1991). | MR | Zbl

[8] M. A. Grinfeld, Stress driven instabilities in crystals: mathematical models and physical manifestations. J. Nonlinear Sci. 3 (1993) 35-83. | MR | Zbl

[9] M. A. Grinfeld, Manifestations of the stress driven rearrangement instabilities in creep, damaging and fracture. Final Report.Wright-Patterson Laboratory (1995).

[10] MSR Bulletin (1996).

[11] L. D. Landau and E. M. Lifshitz, Statistical physics, Part 1. Oxford, Pergamon Press (1986). | JFM | MR | Zbl

[12] P. Nozières, Lectures at Collège de France (1988) unpublished notes. Growth and Shape of Crystals (lectures given at Beg-Rohu Summer School, Brittany, 1989) in Solids Far From Equilibrium, C. Godreche Ed., Cambridge University Press (1991).

[13] P. Nozières, Amplitude Expansion for the Grinfeld Instability due to Uniaxial Stress at a Solid Surface. J. Phys. 3 (1993) 681.