A Talenti comparison result for a class of Neumann boundary value problems
A Celentano, C Nitsch, C Trombetti - arXiv preprint arXiv:2405.05392, 2024 - arxiv.org
A Celentano, C Nitsch, C Trombetti
arXiv preprint arXiv:2405.05392, 2024•arxiv.orgIn this paper, we establish a comparison principle in terms of Lorentz norms and point-wise
inequalities between a positive solution $ u $ to the Poisson equation with non-
homogeneous Neumann boundary conditions and a specific positive solution $ v $ to the
Schwartz symmetrized problem, which is related to $ u $ through an additional boundary
condition.
inequalities between a positive solution $ u $ to the Poisson equation with non-
homogeneous Neumann boundary conditions and a specific positive solution $ v $ to the
Schwartz symmetrized problem, which is related to $ u $ through an additional boundary
condition.
In this paper, we establish a comparison principle in terms of Lorentz norms and point-wise inequalities between a positive solution to the Poisson equation with non-homogeneous Neumann boundary conditions and a specific positive solution to the Schwartz symmetrized problem, which is related to through an additional boundary condition.
arxiv.org