2020
DOI: 10.1007/s00208-020-02093-3
|View full text |Cite
|
Sign up to set email alerts
|

An annulus multiplier and applications to the limiting absorption principle for Helmholtz equations with a step potential

Abstract: We consider the Helmholtz equation −∆u + V u − λ u = f on R n where the potential V : R n → R is constant on each of the half-spaces R n−1 ×(−∞, 0) and R n−1 ×(0, ∞). We prove an L p − L q-Limiting Absorption Principle for frequencies λ > max V with the aid of Fourier Restriction Theory and derive the existence of nontrivial solutions of linear and nonlinear Helmholtz equations. As a main analytical tool we develop new L p − L q estimates for a singular Fourier multiplier supported in an annulus.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

0
0
0

Publication Types

Select...

Relationship

0
0

Authors

Journals

citations
Cited by 0 publications
references
References 43 publications
0
0
0
Order By: Relevance

No citations

Set email alert for when this publication receives citations?