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Integral Representation of Functionals in Space of Special Functions with Bounded Deformation


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Integral Representation of Functionals in Space of Special Functions with Bounded Deformation
LV Zhong-xue12ZHENG Li3
1.School of Sciences,NUST,Nanjing 210094,China;2.School of Mathematical Science,Xuzhou Normal University,Xuzhou 221116,China;3.Department of Fundamental Courses,Shandong Vocational and Trade College,Jining 272017,China
space of special functions with bounded deformation integral functionals integral representation
The integral representation is studied in the space of special functions of bounded deformation,of the energy ∫Ωf(x,εu(x))dx,with respect to L1-convergence.Here integrand f satisfies linear growth and coercivity conditions and other special conditions.First,by using some properties of functional,the approximate differentiability of function and the special condition of integrand,integral representation of the volume term is obtained.Secondly,by using the continuity of trace operator,etc.,integral representation of the surface term is obtained,and integral representations of functionals are obtained.


[1] Barroso A C, Fonseca I, Toader R. A relaxation theo?? rem in the space of functions o f bounded defo rma tion [ J]. Ann Scuo laNo rm Sup Pisa C I Sc ,i 2000, 29: 19 - 49.
[2] Ebobisse F, ToaderR. A note on the integra l represen?? tation of functionals in the space SBD( ) [ J]. Rend i?? conti d iM atematica Serie ? , 2003, 23: 189- 201.
[3] Am bro sio L, Cosica A, Da lM aso G. F ine properties of functions w ith bounded de form ation [ J] . Arch Rat M ech Ana,l 1997, 199: 201- 238.
[4] M atth ies H, Strang G, Christiansen E. The sadd le po in t of a d ifferentia l program: energy m ethods in fi?? nite e lem en t ana lysis[M ]. N ew York: W iley, 1979.
[5] Anze llottiG, G iaqu intaM. Ex istence o f the d isp lace?? m ent fie ld for an e lasto??plastic body sub ject to H encky+ s law and Von M ises+ y ie ld cond ition [ J]. M anuscriptaM a th, 1980, 32: 101- 131.
[6] Kohn R V. New estmi ates for deformations in terms o f the ir stra ins[ D]. Princeton: Pr inceton University, 1979.
[7] Suquet PM. Un espace fonctionne l pou r les equations de la plastic ite [ J] . Ann Fac Sci Toulouse, 1979 ( 1): 77- 87.
[8] Tem am R. Problem sM athema tiques en plasticite[M ]. Par is: Gauth ier??V illars, 1983.
[9] Fonseca I, M ller S. Relax ation o f quasiconvex func?? tionals in BV ( ??, Rp ) [ J] . Arch Rat M ech Ana,l 1993, 123, 1- 49.
[10] Be llettini G, Co sc ia A, DalM aso G. Special functions of bounded de form ation[ J]. M a th Z, 1998, 228, 337 - 351.
[11] Bouchitte G, Fonseca I, M ascarenhas L. A g loba l m ethod for re laxa tion[ J] . A rch Ra tM ech Ana,l 1998 ( 145): 45- 68.


Last Update: 2008-04-30