A Talenti comparison result for a weighted Poisson equation with Neumann boundary value
摘要
In this paper, we establish a comparison theorem between positive solutions of the weighted Poisson equation with nonhomogeneous Neumann boundary conditions and suitable positive solutions of its Schwarz symmetrized problem satisfying appropriate matching boundary conditions. We also prove comparison results for the weighted Poisson equation with homogeneous Neumann boundary conditions. Our main tools include weighted isoperimetric inequalities and symmetrization techniques.