This paper relates the lower semi-continuity of an integral functional in the compensated compactness setting of vector fields satisfying a constant-rank first-order differential constraint, to closed đ-p quasiconvexity of the integrand. The lower semi-continuous envelope of relaxation is identified for continuous, but potentially extended real-valued integrands. We discuss the continuity assumption and show that when it is dropped our notion of quasiconvexity is still equivalent to lower semi-continuity of the integrand under an additional assumption on the characteristic cone of đ.
Accepted:
DOI: 10.1051/cocv/2017062
Keywords: Closed A-p quasiconvexity, extended real-valued integrands, semi-continuity, Young measures, relaxation
@article{COCV_2018__24_4_1605_0, author = {Prosinski, Adam}, title = {Closed đ-p {Quasiconvexity} and {Variational} {Problems} with {Extended} {Real-Valued} {Integrands}}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1605--1624}, publisher = {EDP-Sciences}, volume = {24}, number = {4}, year = {2018}, doi = {10.1051/cocv/2017062}, zbl = {1417.49012}, mrnumber = {3922436}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017062/} }
TY - JOUR AU - Prosinski, Adam TI - Closed đ-p Quasiconvexity and Variational Problems with Extended Real-Valued Integrands JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1605 EP - 1624 VL - 24 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017062/ DO - 10.1051/cocv/2017062 LA - en ID - COCV_2018__24_4_1605_0 ER -
%0 Journal Article %A Prosinski, Adam %T Closed đ-p Quasiconvexity and Variational Problems with Extended Real-Valued Integrands %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1605-1624 %V 24 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017062/ %R 10.1051/cocv/2017062 %G en %F COCV_2018__24_4_1605_0
Prosinski, Adam. Closed đ-p Quasiconvexity and Variational Problems with Extended Real-Valued Integrands. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 4, pp. 1605-1624. doi : 10.1051/cocv/2017062. http://archive.numdam.org/articles/10.1051/cocv/2017062/
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