By Claudio Baiocchi (auth.), Gianfranco Capriz, Guido Stampacchia (eds.)
C. Baiocchi: Problèmes � frontière libre liés � des questions d’hydraulique.- Ch. Castaing: Intégrales convexes duales.- G. Duvaut: Etude de problèmes unilateraux en mécanique par des méthodes variationnelles.- D. Kinderlehrer: feedback concerning the loose barriers taking place in variational inequalities.- H. Lanchon: Torsion élastoplastique d’arbres cylindriques: problèmes ouverts.- J.M. Lasry: Dualité en calcul des variations.- J.J. Moreau: On unilateral constraints, friction and plasticity.- B. Nayroles: aspect de vue algébrique. Convexité et intégrantes convexes en mécanique des solides.- W. Noll: On yes convex units of measures and stages of reacting mixtures.- W. Velte: On complementary variational inequalities.
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Extra resources for New Variational Techniques in Mathematical Physics
Example text
Lions et G. Stampacchia [I], Boucher [I] ) , avec frottement (G. L. Lions [I] [2]), gknkralisation 2 la viscoklasticitk (G. Duvaut rl] , Boucher ii) Plasticit6 avec la loi de Hencky (H. Lanchon [l] [2]), de Prandtl-Reuss (B. Nayrolles [l] [2J, ~lasticitk (G. L. Lions blocage ( W. Prager [lj , F. Lknk [I] ) puis [I] ) . avec la loi J. Moreau [l] [2] 1, Qlastovisco- [q , G. Duvaut [2] ) , matkriaux 2 . iii) Parois semi-permkables (en thermique, mkcanique des fluides en milieux poreux, physique des solutions) (G.
On suppose T une -f - compact mCtrisable. , non partout Cgale B E B valeurs dans g sa duale. On pose +a Alo+s If et Ig sont duales l'une de l'autre, c'est dire, 1 w Vu L If(u) = SUP { - I ( v ) 1 . v E L (T, p ) ) E' g E' E vv E w L 1 ~ 6 v )= sup { E') - If(u) I u E 'L E (T, p ) ) C. C a s t a i n g I1 s u f f i t de v e r i f i e r l a formule Demonstration. I f ( u ) = sup { . ' Quelque s o i e n t u E L; et un element de r < If ( u ) . Soit a , v E LEl - Ig(v) 1 L (T, p ) E m 1.
Dunod 1972 [3]. Problsmes u n i l a t k r a u x d a n s l a t h k o r i e d e s p l a q u e s en G. Duvaut forte flexion. A paraitre au Journal de Mkcanique 1973. 141. Inkquations en Thermoklasticitk et magnktohydrodynamique. Arch. f. Rat. Mech. Anal. Vol 46, n04, 1972, p. 241. G. FICHERA [ I]. Mem. Acad. Naz. Lincei, 8(7), P. GERMAIN [I]. Mkcanique des milieux continus. Masson Paris (19 1. H. LANCHON [ I ] . Probldme dtklastoplasticitkavec la loi de Hencky. 91 Paris, tome 271 (1970), p. 888. S.