A priori estimates and application to the symmetry of solutions for critical p-Laplace equations

Jérôme Vétois (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We establish pointwise a priori estimates for solutions in D-1 (' p) (R-n) of equations of type - Delta pu = f (x, u), where p is an element of (1, n), Delta(p) := div (broken vertical bar del u broken vertical bar(p-2)del u) is the p -Laplace operator, and f is a Caratheodory function with critical Sobolev growth. In the case of positive solutions, our estimates allow us to extend previous radial symmetry results. In particular, by combining our results and a result of DamascelliRamaswamy 161, we are able to extend a recent result of Damascelli-Merchan-Montoro-Sciunzi Pion the symmetry of positive solutions in D1,P (Jr) of the equation -Delta(pu) = u (p* - 1), where p* := n p / (n - p)

Domaines: Equations aux dérivées partielles [math.AP]

Jérôme Vétois. A priori estimates and application to the symmetry of solutions for critical p-Laplace equations. Journal of Differential Equations, 2016, 260 (1), pp.149-161. ⟨10.1016/j.jde.2015.08.041⟩. ⟨hal-01288044⟩