关键词: von Neumann Landau equation, wave functions, Dirichlet problem

Abstract:

In this article, we are concerned with the Dirichlet problem of the stationary von Neumann--Landau wave equation: { ( -Δ_x + Δ_y ) Φ (x, y) = 0,     x, y ∈ Ω
   Φ | _∂Ω×∂Ω = f,
where Ω is a bounded domain in Rⁿ. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.

Key words: von Neumann Landau equation, wave functions, Dirichlet problem