The average-distance problem is to find the best way to approximate (or represent) a given measure μ on by a one-dimensional object. In the penalized form the problem can be stated as follows: given a finite, compactly supported, positive Borel measure μ, minimize
Keywords: Average-distance problem, Nonlocal variational problem, Regularity
@article{AIHPC_2014__31_1_169_0, author = {Slep\v{c}ev, Dejan}, title = {Counterexample to regularity in average-distance problem}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {169--184}, publisher = {Elsevier}, volume = {31}, number = {1}, year = {2014}, doi = {10.1016/j.anihpc.2013.02.004}, mrnumber = {3165284}, zbl = {1286.49055}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2013.02.004/} }
TY - JOUR AU - Slepčev, Dejan TI - Counterexample to regularity in average-distance problem JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 169 EP - 184 VL - 31 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2013.02.004/ DO - 10.1016/j.anihpc.2013.02.004 LA - en ID - AIHPC_2014__31_1_169_0 ER -
%0 Journal Article %A Slepčev, Dejan %T Counterexample to regularity in average-distance problem %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 169-184 %V 31 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2013.02.004/ %R 10.1016/j.anihpc.2013.02.004 %G en %F AIHPC_2014__31_1_169_0
Slepčev, Dejan. Counterexample to regularity in average-distance problem. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 1, pp. 169-184. doi : 10.1016/j.anihpc.2013.02.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2013.02.004/
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