2019/05/02 by Giovanni Catino, Catino, Giovanni, Dario D. Monticelli +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1905.01012
openalex publication_date 2019/05/02 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We prove an existence result for the Poisson equation on non-compact\nRiemannian manifolds satisfying weighted Poincar 'e inequalities outside\ncompact sets. Our result applies to a large class of manifolds including, for\ninstance, all non-parabolic manifolds with minimal positive Green's function\nvanishing at infinity. On the source function we assume a sharp pointwise decay\ndepending on the weight appearing in the Poincar 'e inequality and on the\nbehavior of the Ricci curvature at infinity. We do not require any curvature or\nspectral assumptions on the manifold.\n