Elvira Zappale
Universidade de Salerno

Abstract: By means of duality we prove existence and uniqueness of equilibrium for energies described by integral functionals which fail to be convex. This analysis is motivated by some physical models of elastic materials (cf. for istance [2, 4]) and the techniques generalize the methods first introduced in [5, 1]. A suitable Euler Lagrange equation characterizing the minimizers is derived.

Joint work with G. Carita and G. Pisante

References
[1] AWI, R. & GANGBO, W., A polyconvex integrand; Euler-Lagrange Equations and Uniqueness of Equilibrium ARMA 214 (2014), no. 1, 143–182.
[2] BEATTY, M., Topics in finite elasticity: hyperelasticity of rubber materials, elastomers and biological tissues, with examples, Appl. Mech. Rv. Vol 40, no. 12 (1987) 1700-1734.
[3] CARITA G., PISANTE G., & ZAPPALE E. In preparation.
[4] CONTI S.,& DOLZMANN G. On the Theory of Relaxation in Nonlinear Elasticity with Constraints on the Determinant, ARMA, (2014), doi:10.1007/s00205-014-0835-9.
[5] GANGBO, W. & VAN DER PUTTEN, R. Uniqueness of equilibrium configurations in solid crystals. SIAM Journal on Math. Anal. 32, (3) (2000) 465-492.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.