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Restriction estimates in a conical singular space: Schrödinger equation.
- Source :
-
Forum Mathematicum . Nov2023, Vol. 35 Issue 6, p1707-1725. 19p. - Publication Year :
- 2023
-
Abstract
- This paper continues our previous program to study the restriction estimates in a class of conical singular spaces X = C (Y) = (0 , ∞) r × Y equipped with the metric g = d r 2 + r 2 h , where the cross section Y is a compact (n - 1) -dimensional closed Riemannian manifold (Y , h) . Assuming the initial data possesses additional regularity in the angular variable θ ∈ Y , we prove some linear restriction estimates for the solutions of Schrödinger equations on the cone X. The smallest positive eigenvalue of the operator Δ h + V 0 + (n - 2) 2 / 4 plays an important role in the result. As applications, we prove local energy estimates and Keel–Smith–Sogge estimates for the Schrödinger equation in this setting. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09337741
- Volume :
- 35
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Forum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 173364376
- Full Text :
- https://doi.org/10.1515/forum-2023-0066