In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand $f$ : ${R}^{n}$$\times $${R}^{n}$ $\to $ ${R}^{1}$$\cup $ $\left\{\infty \right\}$, where ${R}^{n}$ is the $n$-dimensional euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.

Keywords: good function, infinite horizon, integrand, overtaking optimal function, turnpike property

@article{COCV_2009__15_4_872_0, author = {Zaslavski, Alexander J.}, title = {Structure of approximate solutions of variational problems with extended-valued convex integrands}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {872--894}, publisher = {EDP-Sciences}, volume = {15}, number = {4}, year = {2009}, doi = {10.1051/cocv:2008053}, mrnumber = {2567250}, zbl = {1175.49002}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008053/} }

TY - JOUR AU - Zaslavski, Alexander J. TI - Structure of approximate solutions of variational problems with extended-valued convex integrands JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 872 EP - 894 VL - 15 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008053/ DO - 10.1051/cocv:2008053 LA - en ID - COCV_2009__15_4_872_0 ER -

%0 Journal Article %A Zaslavski, Alexander J. %T Structure of approximate solutions of variational problems with extended-valued convex integrands %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 872-894 %V 15 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008053/ %R 10.1051/cocv:2008053 %G en %F COCV_2009__15_4_872_0

Zaslavski, Alexander J. Structure of approximate solutions of variational problems with extended-valued convex integrands. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 4, pp. 872-894. doi : 10.1051/cocv:2008053. http://archive.numdam.org/articles/10.1051/cocv:2008053/

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