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- Title
Bôcher-type theorems for the Poisson's equation on manifolds with conical metrics.
- Authors
Wan, Fangshu
- Abstract
We prove a generalized Bôcher-type theorem for the nonhomogeneous Laplace's equations on singular manifolds with conical metrics. More specifically, we give a sharp characterization of the behavior at isolated singularities of a solution bounded on one side for the equation Δ g u = f ( f ∈ L g q with q > n 2 ). The main results in this paper imply that a nonnegative solution with conical singularities has certain of the attributes of fundamental solutions.
- Subjects
POISSON'S equation; LAPLACE'S equation; MANIFOLDS (Mathematics)
- Publication
Calculus of Variations & Partial Differential Equations, 2020, Vol 59, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-020-01775-9