Abstract
We prove the strong unique continuation property for the differential inequality |(∂t + Δ)u(x, t)| ≤ V(x, t)|u(x, t)|, with V contained in weak spaces. In particular, we establish the strong unique continuation property for V ∈ L∞tLd/2,∞x, which has been left open since the works of Escauriaza (2000) and Escauriaza and Vega (2001). Our results are consequences of the Carleman estimates for the heat operator in the Lorentz spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 2257-2274 |
| Number of pages | 18 |
| Journal | Analysis and PDE |
| Volume | 17 |
| Issue number | 7 |
| DOIs | |
| State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open
Keywords
- Carleman estimate
- Hermite operator
- the heat equation
- unique continuation