Let be a function from the real mn-matrices to the real numbers. If is quasiconvex in the sense of the calculus of variations, then we show that can be approximated locally uniformly by quasiconvex polynomials.
Classification : 49J45, 41A10
Mots clés : Stone-Weierstrass theorem, locally uniform convergence
@article{COCV_2008__14_4_795_0, author = {Heinz, Sebastian}, title = {Quasiconvex functions can be approximated by quasiconvex polynomials}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {795--801}, publisher = {EDP-Sciences}, volume = {14}, number = {4}, year = {2008}, doi = {10.1051/cocv:2008010}, zbl = {1148.49012}, mrnumber = {2451797}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2008010/} }
TY - JOUR AU - Heinz, Sebastian TI - Quasiconvex functions can be approximated by quasiconvex polynomials JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 DA - 2008/// SP - 795 EP - 801 VL - 14 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008010/ UR - https://zbmath.org/?q=an%3A1148.49012 UR - https://www.ams.org/mathscinet-getitem?mr=2451797 UR - https://doi.org/10.1051/cocv:2008010 DO - 10.1051/cocv:2008010 LA - en ID - COCV_2008__14_4_795_0 ER -
Heinz, Sebastian. Quasiconvex functions can be approximated by quasiconvex polynomials. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 795-801. doi : 10.1051/cocv:2008010. http://www.numdam.org/articles/10.1051/cocv:2008010/
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