We prove uniform continuity of radially symmetric vector minimizers to multiple integrals on a ball , among the Sobolev functions in , using a jointly convex lsc with even and superlinear. Besides such basic hypotheses, is assumed to satisfy also a geometrical constraint, which we call quasi - scalar; the simplest example being the biradial case . Complete liberty is given for to take the value, so that our minimization problem implicitly also represents e.g. distributed-parameter optimal control problems, on constrained domains, under PDEs or inclusions in explicit or implicit form. While generic radial functions in this Sobolev space oscillate wildly as , our minimizing profile-curve is, in contrast, absolutely continuous and tame, in the sense that its “static level” always increases with , a original feature of our result.
Keywords: vectorial calculus of variations, vectorial distributed-parameter optimal control, continuous radially symmetric monotone minimizers
@article{COCV_2014__20_1_141_0, author = {Bicho, Lu{\'\i}s Balsa and Ornelas, Ant\'onio}, title = {Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {141--157}, publisher = {EDP-Sciences}, volume = {20}, number = {1}, year = {2014}, doi = {10.1051/cocv/2013058}, mrnumber = {3182694}, zbl = {1286.49040}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2013058/} }
TY - JOUR AU - Bicho, Luís Balsa AU - Ornelas, António TI - Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 141 EP - 157 VL - 20 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2013058/ DO - 10.1051/cocv/2013058 LA - en ID - COCV_2014__20_1_141_0 ER -
%0 Journal Article %A Bicho, Luís Balsa %A Ornelas, António %T Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 141-157 %V 20 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2013058/ %R 10.1051/cocv/2013058 %G en %F COCV_2014__20_1_141_0
Bicho, Luís Balsa; Ornelas, António. Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 1, pp. 141-157. doi : 10.1051/cocv/2013058. http://archive.numdam.org/articles/10.1051/cocv/2013058/
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