https://hal-enpc.archives-ouvertes.fr/hal-00674618Lindgren, ErikErikLindgrenCERMICS - Centre d'Enseignement et de Recherche en MathÃ©matiques et Calcul Scientifique - ENPC - Ã‰cole des Ponts ParisTechOn the penalized obstacle problem in the unit half ballHAL CCSD2010obstacle problemelliptic equationregularitypenalization[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Hal, Cermics2012-02-27 17:06:372016-03-21 17:33:392012-02-27 17:06:37enJournal articles1We study the penalized obstacle problem in the unit half ball, i.e. an approximation of the obstacle problem in the unit half ball. The main result states that when the approximation parameter is small enough and when certain level sets are sufficiently close to the hyperplane {x1 = 0}, then these level sets are uniformly C1 regular graphs. As a by-product, we also recover some regularity of the free boundary for the limiting problem, i.e., for the obstacle problem.