A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end.

Keywords: cartesian currents, complex bodies, ground states, multifield theories

@article{COCV_2009__15_2_377_0, author = {Mariano, Paolo Maria and Modica, Giuseppe}, title = {Ground states in complex bodies}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {377--402}, publisher = {EDP-Sciences}, volume = {15}, number = {2}, year = {2009}, doi = {10.1051/cocv:2008036}, mrnumber = {2513091}, zbl = {1161.74006}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008036/} }

TY - JOUR AU - Mariano, Paolo Maria AU - Modica, Giuseppe TI - Ground states in complex bodies JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 377 EP - 402 VL - 15 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008036/ DO - 10.1051/cocv:2008036 LA - en ID - COCV_2009__15_2_377_0 ER -

%0 Journal Article %A Mariano, Paolo Maria %A Modica, Giuseppe %T Ground states in complex bodies %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 377-402 %V 15 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008036/ %R 10.1051/cocv:2008036 %G en %F COCV_2009__15_2_377_0

Mariano, Paolo Maria; Modica, Giuseppe. Ground states in complex bodies. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 2, pp. 377-402. doi : 10.1051/cocv:2008036. http://archive.numdam.org/articles/10.1051/cocv:2008036/

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