A necessary and sufficient condition for -regularity of solutions of one-dimensional variational obstacle problems
Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 103-134.
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In this paper we study the -regularity of solutions of one-dimensional variational obstacle problems in when the obstacles are and the Lagrangian is locally Hölder continuous and globally elliptic. In this framework, we prove that the solutions of one-dimensional variational obstacle problems are for all boundary data if and only if the value function is Lipschitz continuous at all boundary data.
Publié le :
DOI : 10.4171/RSMUP/33
DOI : 10.4171/RSMUP/33
Classification :
49, 00
Mots-clés : One-dimensional variational obstacle problems, $C^1$-regularity, value function, conditional equa-continuity.
Mots-clés : One-dimensional variational obstacle problems, $C^1$-regularity, value function, conditional equa-continuity.
Affiliations des auteurs :
Mandallena, Jean-Philippe 1
@article{RSMUP_2019__142__103_0, author = {Mandallena, Jean-Philippe}, title = {A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {103--134}, publisher = {European Mathematical Society Publishing House}, address = {Zuerich, Switzerland}, volume = {142}, year = {2019}, doi = {10.4171/RSMUP/33}, mrnumber = {4032807}, zbl = {1439.49002}, url = {http://www.numdam.org/articles/10.4171/RSMUP/33/} }
TY - JOUR AU - Mandallena, Jean-Philippe TI - A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2019 SP - 103 EP - 134 VL - 142 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/33/ DO - 10.4171/RSMUP/33 ID - RSMUP_2019__142__103_0 ER -
%0 Journal Article %A Mandallena, Jean-Philippe %T A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems %J Rendiconti del Seminario Matematico della Università di Padova %D 2019 %P 103-134 %V 142 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/33/ %R 10.4171/RSMUP/33 %F RSMUP_2019__142__103_0
Mandallena, Jean-Philippe. A necessary and sufficient condition for $C^1$-regularity of solutions of one-dimensional variational obstacle problems. Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 103-134. doi : 10.4171/RSMUP/33. http://www.numdam.org/articles/10.4171/RSMUP/33/
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