The question of interior blow-up for an elliptic Neumann problem: the critical case

Olivier Rey (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

In contrast with the subcritical case, we prove that for any bounded domain $\Omega$ in $\mathbb{R}^3$, the Neumann elliptic problem with critical nonlinearity $-\Delta u + \mu u = u^{5}$, $u > 0$ in $\Omega$, $\partial u / \partial n= 0$ on $\partial\Omega$ has no solution blowing up at only interior points as μ goes to infinity.

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Rey. The question of interior blow-up for an elliptic Neumann problem: the critical case. Journal de Mathématiques Pures et Appliquées, 2002, 81, pp.655-696. ⟨hal-00935381⟩