Mathematics · Partial Differential Equations

Suppose u = u(x, y) is the solution of the boundary value problem: ∂2u∂x2 + ∂2u∂y2 + ∂u∂x = 0 in the domain {(x, y) ∈ ℝ2 : x2 + y2 < 1}, with the boundary condition u(x, y) = 1 + 2x2y2 on {(x, y) ∈ ℝ2 : x2 + y2 = 1}. Then, by applying the maximum-minimum principle, which of the following statements is true?