Nehari manifold (original) (raw)

In the calculus of variations, a branch of mathematics, a Nehari manifold is a manifold of functions, whose definition is motivated by the work of Zeev Nehari . It is a differentiable manifold associated to the Dirichlet problem for the semilinear elliptic partial differential equation Here Δ is the Laplacian on a bounded domain Ω in Rn. There are infinitely many solutions to this problem. Solutions are precisely the critical points for the energy functional on the Sobolev space H10(Ω). The Nehari manifold is defined to be the set of v ∈ H10(Ω) such that