Small nonlinear Helmholtz equations have solutions with prescribed incoming and outgoing wave patterns at infinity, on Euclidean space and asymptotically conic manifolds, under a dimension-degree condition.
Limiting absorption principle on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We use a Lagrangian perspective to show the limiting absorption principle on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. More precisely we show that, for non-zero spectral parameter, the `on spectrum', as well as the `off-spectrum', spectral family is Fredholm in function spaces which encode the Lagrangian regularity of generalizations of `outgoing spherical waves' of scattering theory, and indeed this persists in the `physical half plane'.
fields
math.AP 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Existence and asymptotics of nonlinear Helmholtz eigenfunctions
Small nonlinear Helmholtz equations have solutions with prescribed incoming and outgoing wave patterns at infinity, on Euclidean space and asymptotically conic manifolds, under a dimension-degree condition.