On the penalized obstacle problem in the unit half ball

Erik Lindgren (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

We 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.

Mots clés: obstacle problem; elliptic equation; regularity; penalization

Domaines: Equations aux dérivées partielles [math.AP]

Erik Lindgren. On the penalized obstacle problem in the unit half ball. Electronic Journal of Differential Equations, 2010, 2010 (9), pp.1-12. ⟨hal-00674618⟩