An elliptic Neumann problem with critical nonlinearity in three dimensional domains

Olivier Rey (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We study an elliptic partial differential equation of second order with critical nonlinearity and Neumann boundary conditions. An improved asymptotic analysis allows us to prove in dimension 3 results previously known in larger dimensional spaces, i.e. existence and multiplicity of concentrated solutions in connection with properties of the mean curvature of the domain boundary.

Mots clés: Nonlinear elliptic PDEs; Critical Sobolev exponent; Noncompact variational problems; Neumann boundary conditions

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Rey. An elliptic Neumann problem with critical nonlinearity in three dimensional domains. Communications in Contemporary Mathematics, 1999, 1 (3), pp.405-449. ⟨hal-00943493⟩