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Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity
- Source :
- Journal of Evolution Equations, Journal of Evolution Equations, 2022, ⟨10.1007/s00028-022-00842-2⟩
- Publication Year :
- 2021
- Publisher :
- HAL CCSD, 2021.
-
Abstract
- 15 pages, 19 ref.; International audience; We prove an inequality of Hölder type traducing the unique continuation property at one time for the heat equation with a potential and Neumann boundary condition. The main feature of the proof is to overcome the propagation of smallness by a global approach using a refined parabolic frequency function method. It relies with a Carleman commutator estimate to obtain the logarithmic convexity property of the frequency function.
Details
- Language :
- English
- ISSN :
- 14243199 and 14243202
- Database :
- OpenAIRE
- Journal :
- Journal of Evolution Equations, Journal of Evolution Equations, 2022, ⟨10.1007/s00028-022-00842-2⟩
- Accession number :
- edsair.doi.dedup.....452a6a73107363e741204d986d74d0e1